WAVES – MCQ SET (25 Questions)

WAVES – MCQ SET (25 Questions)

Q1.

The equation of a transverse wave isy=0.02sin⁡(50t−2x)y = 0.02 \sin(50t – 2x)y=0.02sin(50t−2x)

( SI units )

The wave speed is:

A) 25 m/s
B) 50 m/s
C) 100 m/s
D) 4 m/s

Q2.

Two waves of equal amplitude and frequency travel in opposite directions. The distance between two successive nodes is:

A) λ
B) λ/2
C) λ/4
D) 2λ

Q3.

If tension in a stretched string becomes 4 times, wave speed becomes:

A) 4 times
B) 2 times
C) Half
D) √2 times

Q4.

A sound wave travels from air into water. Which quantity remains unchanged?

A) Speed
B) Frequency
C) Wavelength
D) Intensity

Q5.

The maximum particle velocity in a wave is proportional to:

A) A
B) ω
C) Aω
D) A/ω

Q6.

A pipe closed at one end has fundamental frequency 200 Hz. The next harmonic frequency is:

A) 400 Hz
B) 600 Hz
C) 800 Hz
D) 1000 Hz

Q7.

In Doppler effect, if both source and observer move towards each other, observed frequency:

A) Decreases
B) Remains same
C) Increases
D) Becomes zero

Q8.

Energy transmitted in a wave is proportional to:

A) Amplitude
B) Amplitude²
C) Frequency
D) Wavelength

Q9.

Two waves interfere. If phase difference is π, resultant amplitude is:

A) 2A
B) A
C) Zero
D) √2A

Q10.

Wave speed in string depends on:

A) Amplitude
B) Frequency
C) Tension and linear density
D) Length

Q11.

A wave travels with speed 300 m/s and frequency 500 Hz. Wavelength is:

A) 0.6 m
B) 1.5 m
C) 0.06 m
D) 0.006 m

Q12.

In standing waves, nodes are points of:

A) Maximum displacement
B) Zero displacement
C) Maximum velocity
D) Maximum energy

Q13.

If frequency doubles keeping tension constant, wavelength:

A) Doubles
B) Halves
C) Remains same
D) Becomes 4 times

Q14.

The ratio of velocities of sound in two gases is √2. Ratio of their temperatures (assuming same gas) is:

A) 2
B) 1/2
C) √2
D) 4

Q15.

A wave is represented byy=Asin⁡(ωt+kx)y = A \sin(ωt + kx)y=Asin(ωt+kx)

It is traveling:

A) Along +x
B) Along –x
C) Standing wave
D) Not a wave

Q16.

Beats are produced when two waves have:

A) Same amplitude
B) Slightly different frequencies
C) Same phase
D) Same frequency

Q17.

Intensity of wave increases by factor 9. Amplitude increases by:

A) 9
B) 3
C) 6
D) 81

Q18.

If length of closed pipe is 0.85 m and speed of sound 340 m/s, fundamental frequency is:

A) 50 Hz
B) 100 Hz
C) 200 Hz
D) 400 Hz

Q19.

In stationary wave, energy transport:

A) Occurs forward
B) Occurs backward
C) Zero
D) Depends on amplitude

Q20.

Phase difference between two points separated by λ/4 is:

A) π/4
B) π/2
C) π
D) 2π

Q21.

The group velocity equals phase velocity in:

A) Dispersive medium
B) Non-dispersive medium
C) Water only
D) Air only

Q22.

Sound intensity level increases by 20 dB. Intensity increases by:

A) 10 times
B) 20 times
C) 100 times
D) 200 times

Q23.

If linear density of string doubles, wave speed becomes:

A) Double
B) Half
C) 1/√2 times
D) √2 times

Q24.

Two identical waves in phase superpose. Resultant intensity becomes:

A) I
B) 2I
C) 4I
D) 8I

Q25.

In Doppler effect, if source moves away and observer is stationary, frequency:

A) Increases
B) Decreases
C) No change
D) Becomes zero

Answer

Question No.Answer
1A
2B
3B
4B
5C
6B
7C
8B
9C
10C
11A
12B
13B
14A
15B
16B
17B
18C
19C
20B
21B
22C
23C
24C
25B

Solution

WAVES – DETAILED SOLUTIONS

Q1. Wave speed

Equation: y=0.02sin⁡(50t−2x)y = 0.02 \sin(50t – 2x)y=0.02sin(50t−2x)

Wave equation form: y=Asin⁡(ωt−kx)y = A \sin(\omega t – kx)y=Asin(ωt−kx)v=ωk=502=25 m/sv = \frac{\omega}{k} = \frac{50}{2} = 25 \text{ m/s}v=kω​=250​=25 m/s

Answer: A

Q2. Distance between nodes (standing wave)

Distance between nodes=λ2\text{Distance between nodes} = \frac{\lambda}{2}Distance between nodes=2λ​

Answer: B

Q3. Tension increases 4×

v=Tμv = \sqrt{\frac{T}{\mu}}v=μT​​ v′=4Tμ=2vv’ = \sqrt{\frac{4T}{\mu}} = 2vv′=μ4T​​=2v

Answer: B

Q4. Wave enters new medium (air → water)

Frequency remains constant across media.

Answer: B

Q5. Maximum particle velocity

vparticle,max=ωAv_{particle,max} = \omega Avparticle,max​=ωA

Proportional to AωA\omegaAω

Answer: C

Q6. Pipe closed at one end

Harmonics: odd multiplesf1=200 Hz,f3=3f1=600 Hzf_1 = 200\,\text{Hz}, \quad f_3 = 3f_1 = 600\,\text{Hz}f1​=200Hz,f3​=3f1​=600Hz

Answer: B

Q7. Doppler effect, both moving toward each other

Observed frequency increases

Answer: C

Q8. Energy transmitted in wave

E∝A2E \propto A^2E∝A2

Answer: B

Q9. Two waves interfere with phase π

Destructive interference → amplitude zero

Answer: C

Q10. Wave speed on string

v=Tμv = \sqrt{\frac{T}{\mu}}v=μT​​

Depends on tension and linear density

Answer: C

Q11. Wavelength

v=fλ  ⟹  λ=vf=300500=0.6 mv = f \lambda \implies \lambda = \frac{v}{f} = \frac{300}{500} = 0.6\,\text{m}v=fλ⟹λ=fv​=500300​=0.6m

Answer: A

Q12. Nodes in standing wave

Nodes = points of zero displacement

Answer: B

Q13. Frequency doubles, wavelength (Tension constant)

v=fλ  ⟹  λ=vf  ⟹  λ′=λ2v = f \lambda \implies \lambda = \frac{v}{f} \implies \lambda’ = \frac{\lambda}{2}v=fλ⟹λ=fv​⟹λ′=2λ​

Answer: B

Q14. Sound speed ratio & temperature

v∝T  ⟹  v1v2=T1T2v \propto \sqrt{T} \implies \frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}}v∝T​⟹v2​v1​​=T2​T1​​​

Given v1/v2=2v_1/v_2 = \sqrt{2}v1​/v2​=2​, so T1/T2=2T_1/T_2 = 2T1​/T2​=2

Answer: A

Q15. Wave equation y=Asin⁡(ωt+kx)y = A \sin(\omega t + kx)y=Asin(ωt+kx)

Form sin⁡(ωt+kx)\sin(\omega t + kx)sin(ωt+kx) → wave travels along –x

Answer: B

Q16. Beats produced

Beats occur when two waves of slightly different frequency interfere

Answer: B

Q17. Intensity increases by 9×

I∝A2  ⟹  A′=9A=3AI \propto A^2 \implies A’ = \sqrt{9} A = 3AI∝A2⟹A′=9​A=3A

Answer: B

Q18. Closed pipe fundamental frequency

f1=v4L=3404×0.85=100 Hzf_1 = \frac{v}{4L} = \frac{340}{4 \times 0.85} = 100\,\text{Hz}f1​=4Lv​=4×0.85340​=100Hz

Answer: C

Q19. Energy transport in stationary wave

In standing wave, net energy transport = 0

Answer: C

Q20. Phase difference over λ/4

Δϕ=2πλ⋅λ4=π2\Delta \phi = \frac{2\pi}{\lambda} \cdot \frac{\lambda}{4} = \frac{\pi}{2}Δϕ=λ2π​⋅4λ​=2π​

Answer: B

Q21. Group velocity = phase velocity

Occurs in non-dispersive medium

Answer: B

Q22. Sound intensity increase 20 dB

β=10log⁡10II0  ⟹  20 dB→I/I0=1020/10=100\beta = 10 \log_{10} \frac{I}{I_0} \implies 20\,\text{dB} \to I/I_0 = 10^{20/10} = 100β=10log10​I0​I​⟹20dB→I/I0​=1020/10=100

Answer: C

Q23. Linear density doubles

v=Tμ  ⟹  v′=T2μ=v2v = \sqrt{\frac{T}{\mu}} \implies v’ = \sqrt{\frac{T}{2\mu}} = \frac{v}{\sqrt{2}}v=μT​​⟹v′=2μT​​=2​v​

Answer: C

Q24. Two identical waves in phase

Ares=2A  ⟹  Ires∝(2A)2=4IA_{res} = 2A \implies I_{res} \propto (2A)^2 = 4IAres​=2A⟹Ires​∝(2A)2=4I

Answer: C

Q25. Source moves away, observer stationary

Observed frequency decreases

Answer: B