Grade 11 : Physics - Waves (Set 4)

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Grade 11 : Physics - Waves (Set 4)— Questions & Detailed Solutions

A progressive sinusoidal wave propagates along the positive x-axis according to the displacement function: $y(x,t) = 0.05 \sin(4\pi t - 0.02\pi x)$, where $x$ and $y$ are in meters and $t$ is in seconds.
What is the propagation speed of the wave?

(A)

100 m/s

(B)

200 m/s

(C)

50 m/s

(D)

400 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Comparing with $y = A \sin(\omega t - k x)$, we have $\omega = 4\pi \text{ rad/s}$ and $k = 0.02\pi \text{ rad/m}$.
Wave speed $v = \frac{\omega}{k} = \frac{4\pi}{0.02\pi} = 200 m/s$.

Parameter Value
Length of string ($L$) 2.0 m
Total mass ($M$) 0.02 kg
Applied Tension ($T$) 100 N
Using the experimental parameters given in the table above, determine the speed of a transverse wave traveling along the stretched string.

Parameter	Value
Length of string ($L$)	2.0 m
Total mass ($M$)	0.02 kg
Applied Tension ($T$)	100 N

(A)

50 m/s

(B)

70.7 m/s

(C)

100 m/s

(D)

200 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Linear mass density $\mu = \frac{M}{L} = \frac{0.02}{2.0} = 0.01 \text{ kg/m}$.
Speed of transverse wave $v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{100}{0.01}} = \sqrt{10000} = 100 m/s$.

An open organ pipe of length $L = 0.85 m$ is sounded in air where the velocity of sound is $v = 340 m/s$.
Calculate the fundamental frequency of resonance for this open pipe.

(A)

100 Hz

(B)

200 Hz

(C)

400 Hz

(D)

850 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:For an open organ pipe open at both ends, fundamental frequency $f_1 = \frac{v}{2L}$.
$$f_1 = \frac{340}{2 \times 0.85} = \frac{340}{1.7} = 200 \text{ Hz}$$

A closed organ pipe (pipe closed at one end and open at the other) has a physical length of 0.425 m. Speed of sound in air is 340 m/s.
What is the frequency of the first overtone (3rd harmonic) produced by this pipe?

(A)

200 Hz

(B)

400 Hz

(C)

600 Hz

(D)

800 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:For a closed pipe, allowed frequencies are odd harmonics: $f_n = \frac{n v}{4L}$ for $n = 1, 3, 5, ...$
First overtone corresponds to $n = 3$:
$$f_3 = \frac{3 \times 340}{4 \times 0.425} = \frac{1020}{1.7} = 600 \text{ Hz}$$

Two tuning forks, A and B, are sounded together and produce 5 beats per second. Tuning fork A has a known frequency of 256 Hz. When a small piece of wax is attached to prong B, the beat frequency decreases to 2 beats per second.
What was the original frequency of tuning fork B before wax was added?

(A)

251 Hz

(B)

261 Hz

(C)

263 Hz

(D)

249 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Possible original frequencies for B are $256 \pm 5 = 261 \text{ Hz}$ or 251 Hz.
Adding wax decreases frequency of B.
If $f_B = 261 \text{ Hz}$, decreasing $f_B$ brings it closer to 256 Hz, reducing beat frequency ($261 - 256 = 5 \rightarrow 258 - 256 = 2$).
Hence, original frequency of B was 261 Hz.

Source S1 o--------------------- P
Source S2 o------------------------- P
Path Difference: Δx = 0.1 m | Wavelength: λ = 0.4 m
Two coherent wave sources generate waves of wavelength $\lambda = 0.4 m$. What is the phase difference between the waves arriving at a point P where the path difference is 0.1 m?

(A)

π/4 rad

(B)

π/2 rad

(C)

π rad

(D)

2π rad

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Phase difference $\Delta \phi = \frac{2\pi}{\lambda} \Delta x$.
$$\Delta \phi = \frac{2\pi}{0.4} \times 0.1 = \frac{2\pi}{4} = \frac{\pi}{2} \text{ rad}$$

Helium gas is kept under standard atmospheric pressure $P = 1.01 \times 10^5 \text{ Pa}$ with mass density $\rho = 0.179 \text{ kg/m}^3$. The adiabatic ratio for helium is $\gamma = 5/3$.
Using Laplace's formula $v = \sqrt{\frac{\gamma P}{\rho}}$, calculate the speed of sound in helium gas.

(A)

332 m/s

(B)

480 m/s

(C)

970 m/s

(D)

1250 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:$$v = \sqrt{\frac{(5/3) \times 1.01 \times 10^5}{0.179}} = \sqrt{\frac{1.6833 \times 10^5}{0.179}} = \sqrt{940409.68} \approx 970 \text{ m/s}$$

Two sound waves, A and B, propagate through the same medium. The amplitude of wave A is 3 times the amplitude of wave B.
If the intensity of wave B is $I_0$, what is the intensity of wave A?

(A)

3 I₀

(B)

6 I₀

(C)

9 I₀

(D)

27 I₀

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Intensity of a wave is proportional to the square of its amplitude ($I \propto A^2$).
$$\frac{I_A}{I_B} = \left(\frac{A_A}{A_B}\right)^2 = 3^2 = 9 \implies I_A = 9 I_0$$

A string of length $L = 1.2 m$ is fixed firmly at both ends and vibrates in its third harmonic mode (3 standing loops).
What is the distance between any two consecutive nodes in this standing wave pattern?

(A)

0.2 m

(B)

0.4 m

(C)

0.6 m

(D)

0.8 m

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:For the 3rd harmonic, $L = 3 \left(\frac{\lambda}{2}\right)$.
Distance between consecutive nodes is $\frac{\lambda}{2} = \frac{L}{3} = \frac{1.2}{3} = 0.4 m$.

Q10

An incident transverse wave given by $y_i = A \sin(kx - \omega t)$ travels along a stretched string toward a fixed rigid boundary located at $x = 0$.
Which equation correctly represents the reflected wave $y_r$?

(A)

y_r = A sin(kx + ωt)

(B)

y_r = -A sin(kx + ωt)

(C)

y_r = -A sin(kx - ωt)

(D)

y_r = A cos(kx + ωt)

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Reflection at a rigid boundary causes a phase change of $\pi$ radians and reverses the direction of propagation.
$$y_r = A \sin(-kx - \omega t + \pi) = -A \sin(kx + \omega t)$$

Q11

The speed of sound in air is known to be $v_0 = 332 m/s$ at $T_0 = 0^\circ\text{C}$ (273 K).
What is the speed of sound in air when the temperature rises to $27^\circ\text{C}$ (300 K)?

(A)

340 m/s

(B)

348 m/s

(C)

365 m/s

(D)

380 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Speed of sound in ideal gas depends on absolute temperature: $v \propto \sqrt{T}$.
$$v = v_0 \sqrt{\frac{T}{T_0}} = 332 \times \sqrt{\frac{300}{273}} = 332 \times 1.0483 \approx 348 \text{ m/s}$$

Q12

A emergency vehicle moves at a constant speed of $v_s = 20 m/s$ directly toward a stationary pedestrian while emitting sound at frequency $f = 600 \text{ Hz}$. Speed of sound in air is $v = 340 m/s$.
What frequency does the stationary pedestrian hear?

(A)

566.7 Hz

(B)

600.0 Hz

(C)

637.5 Hz

(D)

670.0 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Using Doppler effect formula for source approaching stationary observer:
$$f' = f \left(\frac{v}{v - v_s}\right) = 600 \times \left(\frac{340}{340 - 20}\right) = 600 \times \frac{340}{320} = 637.5 \text{ Hz}$$

Q13

Resonance Tube Setup:
First Resonance Length: L1 = 16 cm
Second Resonance Length: L2 = 50 cm
In a resonance tube experiment with a tuning fork, the first two resonance positions are found at lengths $L_1 = 16 cm$ and $L_2 = 50 cm$. Calculate the wavelength $\lambda$ of the sound wave.

(A)

34 cm

(B)

68 cm

(C)

100 cm

(D)

136 cm

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Accounting for end correction $e$: $L_1 + e = \frac{\lambda}{4}$ and $L_2 + e = \frac{3\lambda}{4}$.
Subtracting the two equations gives $L_2 - L_1 = \frac{\lambda}{2} \implies \lambda = 2(L_2 - L_1)$.
$$\lambda = 2(50 - 16) = 2 \times 34 = 68 \text{ cm}$$

Q14

Two coherent sinusoidal waves with amplitudes $A_1 = 3 cm$ and $A_2 = 4 cm$ meet at a point in space with a mutual phase difference of $\phi = \frac{\pi}{2}$ radians.
What is the amplitude of the resultant wave formed by superposition?

(A)

1 cm

(B)

5 cm

(C)

7 cm

(D)

12 cm

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Resultant amplitude $A_r = \sqrt{A_1^2 + A_2^2 + 2 A_1 A_2 \cos\phi}$.
For $\phi = \frac{\pi}{2}$, $\cos(\pi/2) = 0$:
$$A_r = \sqrt{3^2 + 4^2 + 0} = \sqrt{9 + 16} = 5 \text{ cm}$$

Q15

A sonometer wire of length $L$ and linear density $\mu$ produces a fundamental frequency of 200 Hz under tension $T$.
If the tension is increased to $4T$ while keeping length and linear density constant, what is the new fundamental frequency?

(A)

100 Hz

(B)

200 Hz

(C)

400 Hz

(D)

800 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Fundamental frequency $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}} \implies f \propto \sqrt{T}$.
$$\frac{f_2}{f_1} = \sqrt{\frac{4T}{T}} = 2 \implies f_2 = 2 \times 200 = 400 \text{ Hz}$$

Q16

A wave traveling along a string is defined by the displacement relation: $y(x,t) = 0.1 \sin(100\pi t - 2\pi x)$ (SI units).
What is the maximum transverse velocity of any particle in the string?

(A)

31.4 m/s

(B)

6.28 m/s

(C)

50.0 m/s

(D)

314 m/s

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:Particle velocity $v_p = \frac{\partial y}{\partial t} = (0.1)(100\pi) \cos(100\pi t - 2\pi x)$.
Maximum particle velocity $v_{p,\text{max}} = A\omega = 0.1 \times 100\pi = 10\pi \approx 31.4 m/s$.

Q17

Pipe A is open at both ends with length $L_O$. Pipe B is closed at one end with length $L_C$. Both pipes have the exact same fundamental frequency of sound.
What is the ratio of their lengths, $\frac{L_O}{L_C}$?

(A)

0.5

(B)

1.0

(C)

1.5

(D)

2.0

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation:Fundamental frequency open pipe $f_O = \frac{v}{2 L_O}$.
Fundamental frequency closed pipe $f_C = \frac{v}{4 L_C}$.
Equating frequencies: $\frac{v}{2 L_O} = \frac{v}{4 L_C} \implies 2 L_O = 4 L_C \implies \frac{L_O}{L_C} = 2$.

Q18

Consider a harmonic wave transmitting energy along a stretched string of linear density $\mu$ with wave speed $v$, frequency $f$, and amplitude $A$.
The average power transmitted by the wave is directly proportional to which parameters?

(A)

f A

(B)

f² A

(C)

f A²

(D)

f² A²

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation:Average power transmitted by a harmonic string wave is $P = \frac{1}{2}\mu v \omega^2 A^2 = 2\pi^2 \mu v f^2 A^2$.
Therefore, power $P$ is directly proportional to $f^2 A^2$.

Q19

Tuning fork A of frequency 440 Hz and tuning fork B are sounded together, producing 4 beats per second. When fork B is filed slightly, the beat frequency increases to 6 beats per second.
What was the original frequency of tuning fork B before filing?

(A)

436 Hz

(B)

440 Hz

(C)

444 Hz

(D)

446 Hz

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Original $f_B = 440 \pm 4 = 444 \text{ Hz}$ or 436 Hz.
Filing increases the frequency of fork B.
If $f_B = 444 \text{ Hz}$, increasing $f_B$ increases the beat frequency $|440 - f_B'|$ (e.g. from 4 to 6).
Thus, original frequency of B was 444 Hz.

Q20

String Segment 1 (v1 = 120 m/s) === Junction === String Segment 2 (v2 = 80 m/s)
A wave of frequency $f = 240 \text{ Hz}$ travels along Segment 1 and enters Segment 2 where the wave velocity drops to $v_2 = 80 m/s$. What is the wavelength $\lambda_2$ in Segment 2?

(A)

0.33 m

(B)

0.50 m

(C)

1.50 m

(D)

3.00 m

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:Frequency remains constant across different media during refraction: $f = 240 \text{ Hz}$.
Wavelength in Segment 2 is given by:
$$\lambda_2 = \frac{v_2}{f} = \frac{80}{240} = \frac{1}{3} \approx 0.33 \text{ m}$$

Grade 11 : Physics - Waves (Set 4)

Grade 11 : Physics - Waves (Set 4)— Questions & Detailed Solutions

A progressive sinusoidal wave propagates along the positive x-axis according to the displacement function: $y(x,t) = 0.05 \sin(4\pi t - 0.02\pi x)$, where $x$ and $y$ are in meters and $t$ is in seconds.
What is the propagation speed of the wave?

Parameter Value
Length of string ($L$) 2.0 m
Total mass ($M$) 0.02 kg
Applied Tension ($T$) 100 N
Using the experimental parameters given in the table above, determine the speed of a transverse wave traveling along the stretched string.

An open organ pipe of length $L = 0.85 m$ is sounded in air where the velocity of sound is $v = 340 m/s$.
Calculate the fundamental frequency of resonance for this open pipe.

A closed organ pipe (pipe closed at one end and open at the other) has a physical length of 0.425 m. Speed of sound in air is 340 m/s.
What is the frequency of the first overtone (3rd harmonic) produced by this pipe?

Two tuning forks, A and B, are sounded together and produce 5 beats per second. Tuning fork A has a known frequency of 256 Hz. When a small piece of wax is attached to prong B, the beat frequency decreases to 2 beats per second.
What was the original frequency of tuning fork B before wax was added?

Helium gas is kept under standard atmospheric pressure $P = 1.01 \times 10^5 \text{ Pa}$ with mass density $\rho = 0.179 \text{ kg/m}^3$. The adiabatic ratio for helium is $\gamma = 5/3$.
Using Laplace's formula $v = \sqrt{\frac{\gamma P}{\rho}}$, calculate the speed of sound in helium gas.

Two sound waves, A and B, propagate through the same medium. The amplitude of wave A is 3 times the amplitude of wave B.
If the intensity of wave B is $I_0$, what is the intensity of wave A?

A string of length $L = 1.2 m$ is fixed firmly at both ends and vibrates in its third harmonic mode (3 standing loops).
What is the distance between any two consecutive nodes in this standing wave pattern?

An incident transverse wave given by $y_i = A \sin(kx - \omega t)$ travels along a stretched string toward a fixed rigid boundary located at $x = 0$.
Which equation correctly represents the reflected wave $y_r$?

The speed of sound in air is known to be $v_0 = 332 m/s$ at $T_0 = 0^\circ\text{C}$ (273 K).
What is the speed of sound in air when the temperature rises to $27^\circ\text{C}$ (300 K)?

A emergency vehicle moves at a constant speed of $v_s = 20 m/s$ directly toward a stationary pedestrian while emitting sound at frequency $f = 600 \text{ Hz}$. Speed of sound in air is $v = 340 m/s$.
What frequency does the stationary pedestrian hear?

Resonance Tube Setup:
First Resonance Length: L1 = 16 cm
Second Resonance Length: L2 = 50 cm
In a resonance tube experiment with a tuning fork, the first two resonance positions are found at lengths $L_1 = 16 cm$ and $L_2 = 50 cm$. Calculate the wavelength $\lambda$ of the sound wave.

Two coherent sinusoidal waves with amplitudes $A_1 = 3 cm$ and $A_2 = 4 cm$ meet at a point in space with a mutual phase difference of $\phi = \frac{\pi}{2}$ radians.
What is the amplitude of the resultant wave formed by superposition?

A sonometer wire of length $L$ and linear density $\mu$ produces a fundamental frequency of 200 Hz under tension $T$.
If the tension is increased to $4T$ while keeping length and linear density constant, what is the new fundamental frequency?

A wave traveling along a string is defined by the displacement relation: $y(x,t) = 0.1 \sin(100\pi t - 2\pi x)$ (SI units).
What is the maximum transverse velocity of any particle in the string?

Pipe A is open at both ends with length $L_O$. Pipe B is closed at one end with length $L_C$. Both pipes have the exact same fundamental frequency of sound.
What is the ratio of their lengths, $\frac{L_O}{L_C}$?

Consider a harmonic wave transmitting energy along a stretched string of linear density $\mu$ with wave speed $v$, frequency $f$, and amplitude $A$.
The average power transmitted by the wave is directly proportional to which parameters?

Tuning fork A of frequency 440 Hz and tuning fork B are sounded together, producing 4 beats per second. When fork B is filed slightly, the beat frequency increases to 6 beats per second.
What was the original frequency of tuning fork B before filing?

String Segment 1 (v1 = 120 m/s) === Junction === String Segment 2 (v2 = 80 m/s)
A wave of frequency $f = 240 \text{ Hz}$ travels along Segment 1 and enters Segment 2 where the wave velocity drops to $v_2 = 80 m/s$. What is the wavelength $\lambda_2$ in Segment 2?

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Grade 11 : Physics - Waves (Set 4)

Grade 11 : Physics - Waves (Set 4)— Questions & Detailed Solutions

A progressive sinusoidal wave propagates along the positive x-axis according to the displacement function: $y(x,t) = 0.05 \sin(4\pi t - 0.02\pi x)$, where $x$ and $y$ are in meters and $t$ is in seconds.What is the propagation speed of the wave?

ParameterValueLength of string ($L$)2.0 mTotal mass ($M$)0.02 kgApplied Tension ($T$)100 NUsing the experimental parameters given in the table above, determine the speed of a transverse wave traveling along the stretched string.

An open organ pipe of length $L = 0.85 m$ is sounded in air where the velocity of sound is $v = 340 m/s$.Calculate the fundamental frequency of resonance for this open pipe.

A closed organ pipe (pipe closed at one end and open at the other) has a physical length of 0.425 m. Speed of sound in air is 340 m/s.What is the frequency of the first overtone (3rd harmonic) produced by this pipe?

Two tuning forks, A and B, are sounded together and produce 5 beats per second. Tuning fork A has a known frequency of 256 Hz. When a small piece of wax is attached to prong B, the beat frequency decreases to 2 beats per second.What was the original frequency of tuning fork B before wax was added?

Helium gas is kept under standard atmospheric pressure $P = 1.01 \times 10^5 \text{ Pa}$ with mass density $\rho = 0.179 \text{ kg/m}^3$. The adiabatic ratio for helium is $\gamma = 5/3$.Using Laplace's formula $v = \sqrt{\frac{\gamma P}{\rho}}$, calculate the speed of sound in helium gas.

Two sound waves, A and B, propagate through the same medium. The amplitude of wave A is 3 times the amplitude of wave B.If the intensity of wave B is $I_0$, what is the intensity of wave A?

A string of length $L = 1.2 m$ is fixed firmly at both ends and vibrates in its third harmonic mode (3 standing loops).What is the distance between any two consecutive nodes in this standing wave pattern?

An incident transverse wave given by $y_i = A \sin(kx - \omega t)$ travels along a stretched string toward a fixed rigid boundary located at $x = 0$.Which equation correctly represents the reflected wave $y_r$?

The speed of sound in air is known to be $v_0 = 332 m/s$ at $T_0 = 0^\circ\text{C}$ (273 K).What is the speed of sound in air when the temperature rises to $27^\circ\text{C}$ (300 K)?

A emergency vehicle moves at a constant speed of $v_s = 20 m/s$ directly toward a stationary pedestrian while emitting sound at frequency $f = 600 \text{ Hz}$. Speed of sound in air is $v = 340 m/s$.What frequency does the stationary pedestrian hear?

Resonance Tube Setup:First Resonance Length: L1 = 16 cmSecond Resonance Length: L2 = 50 cmIn a resonance tube experiment with a tuning fork, the first two resonance positions are found at lengths $L_1 = 16 cm$ and $L_2 = 50 cm$. Calculate the wavelength $\lambda$ of the sound wave.

Two coherent sinusoidal waves with amplitudes $A_1 = 3 cm$ and $A_2 = 4 cm$ meet at a point in space with a mutual phase difference of $\phi = \frac{\pi}{2}$ radians.What is the amplitude of the resultant wave formed by superposition?

A sonometer wire of length $L$ and linear density $\mu$ produces a fundamental frequency of 200 Hz under tension $T$.If the tension is increased to $4T$ while keeping length and linear density constant, what is the new fundamental frequency?

A wave traveling along a string is defined by the displacement relation: $y(x,t) = 0.1 \sin(100\pi t - 2\pi x)$ (SI units).What is the maximum transverse velocity of any particle in the string?

Pipe A is open at both ends with length $L_O$. Pipe B is closed at one end with length $L_C$. Both pipes have the exact same fundamental frequency of sound.What is the ratio of their lengths, $\frac{L_O}{L_C}$?

Consider a harmonic wave transmitting energy along a stretched string of linear density $\mu$ with wave speed $v$, frequency $f$, and amplitude $A$.The average power transmitted by the wave is directly proportional to which parameters?

Tuning fork A of frequency 440 Hz and tuning fork B are sounded together, producing 4 beats per second. When fork B is filed slightly, the beat frequency increases to 6 beats per second.What was the original frequency of tuning fork B before filing?

String Segment 1 (v1 = 120 m/s) === Junction === String Segment 2 (v2 = 80 m/s)A wave of frequency $f = 240 \text{ Hz}$ travels along Segment 1 and enters Segment 2 where the wave velocity drops to $v_2 = 80 m/s$. What is the wavelength $\lambda_2$ in Segment 2?

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A progressive sinusoidal wave propagates along the positive x-axis according to the displacement function: $y(x,t) = 0.05 \sin(4\pi t - 0.02\pi x)$, where $x$ and $y$ are in meters and $t$ is in seconds.
What is the propagation speed of the wave?

Parameter Value
Length of string ($L$) 2.0 m
Total mass ($M$) 0.02 kg
Applied Tension ($T$) 100 N
Using the experimental parameters given in the table above, determine the speed of a transverse wave traveling along the stretched string.

An open organ pipe of length $L = 0.85 m$ is sounded in air where the velocity of sound is $v = 340 m/s$.
Calculate the fundamental frequency of resonance for this open pipe.

A closed organ pipe (pipe closed at one end and open at the other) has a physical length of 0.425 m. Speed of sound in air is 340 m/s.
What is the frequency of the first overtone (3rd harmonic) produced by this pipe?

Two tuning forks, A and B, are sounded together and produce 5 beats per second. Tuning fork A has a known frequency of 256 Hz. When a small piece of wax is attached to prong B, the beat frequency decreases to 2 beats per second.
What was the original frequency of tuning fork B before wax was added?

Helium gas is kept under standard atmospheric pressure $P = 1.01 \times 10^5 \text{ Pa}$ with mass density $\rho = 0.179 \text{ kg/m}^3$. The adiabatic ratio for helium is $\gamma = 5/3$.
Using Laplace's formula $v = \sqrt{\frac{\gamma P}{\rho}}$, calculate the speed of sound in helium gas.

Two sound waves, A and B, propagate through the same medium. The amplitude of wave A is 3 times the amplitude of wave B.
If the intensity of wave B is $I_0$, what is the intensity of wave A?

A string of length $L = 1.2 m$ is fixed firmly at both ends and vibrates in its third harmonic mode (3 standing loops).
What is the distance between any two consecutive nodes in this standing wave pattern?

An incident transverse wave given by $y_i = A \sin(kx - \omega t)$ travels along a stretched string toward a fixed rigid boundary located at $x = 0$.
Which equation correctly represents the reflected wave $y_r$?

The speed of sound in air is known to be $v_0 = 332 m/s$ at $T_0 = 0^\circ\text{C}$ (273 K).
What is the speed of sound in air when the temperature rises to $27^\circ\text{C}$ (300 K)?

A emergency vehicle moves at a constant speed of $v_s = 20 m/s$ directly toward a stationary pedestrian while emitting sound at frequency $f = 600 \text{ Hz}$. Speed of sound in air is $v = 340 m/s$.
What frequency does the stationary pedestrian hear?

Resonance Tube Setup:
First Resonance Length: L1 = 16 cm
Second Resonance Length: L2 = 50 cm
In a resonance tube experiment with a tuning fork, the first two resonance positions are found at lengths $L_1 = 16 cm$ and $L_2 = 50 cm$. Calculate the wavelength $\lambda$ of the sound wave.

Two coherent sinusoidal waves with amplitudes $A_1 = 3 cm$ and $A_2 = 4 cm$ meet at a point in space with a mutual phase difference of $\phi = \frac{\pi}{2}$ radians.
What is the amplitude of the resultant wave formed by superposition?

A sonometer wire of length $L$ and linear density $\mu$ produces a fundamental frequency of 200 Hz under tension $T$.
If the tension is increased to $4T$ while keeping length and linear density constant, what is the new fundamental frequency?

A wave traveling along a string is defined by the displacement relation: $y(x,t) = 0.1 \sin(100\pi t - 2\pi x)$ (SI units).
What is the maximum transverse velocity of any particle in the string?

Pipe A is open at both ends with length $L_O$. Pipe B is closed at one end with length $L_C$. Both pipes have the exact same fundamental frequency of sound.
What is the ratio of their lengths, $\frac{L_O}{L_C}$?

Consider a harmonic wave transmitting energy along a stretched string of linear density $\mu$ with wave speed $v$, frequency $f$, and amplitude $A$.
The average power transmitted by the wave is directly proportional to which parameters?

Tuning fork A of frequency 440 Hz and tuning fork B are sounded together, producing 4 beats per second. When fork B is filed slightly, the beat frequency increases to 6 beats per second.
What was the original frequency of tuning fork B before filing?

String Segment 1 (v1 = 120 m/s) === Junction === String Segment 2 (v2 = 80 m/s)
A wave of frequency $f = 240 \text{ Hz}$ travels along Segment 1 and enters Segment 2 where the wave velocity drops to $v_2 = 80 m/s$. What is the wavelength $\lambda_2$ in Segment 2?