Choose the correct answers

Waves (Physics)

Multiple Choice Questions:

1. A student tunes his guitar by striking a 120 Hertz with a tuning fork, and simultaneously plays the 4th string on his guitar. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which of the following frequencies is the most likely the frequency of the 4th string on his guitar?.

a) 130

b) 117

c) 110

d) 120

Answer: b) 117

Solution:

n = │ f₁ − f₂│

3 = 120 − f₂

 f₂ = 117

2. A transverse wave moves from a medium A to a medium B. In medium A, the velocity of the transverse wave is 500 ms-1 and the wavelength is 5 m. The frequency and the wavelength of the wave in medium B when its velocity is 600 ms-1, respectively are

a) 120 Hz and 5 m

b) 100 Hz and 5 m

c) 120 Hz and 6 m

d) 100 Hz and 6 m

Answer : d) 100 Hz and 6 m

Solution:

f = v / λ ;

f_A = v_A / λ_A

f_A = 500 / 5 = 100 Hz.

When a wave moves from one medium to another medium frequency remains constant.

f_A = f_B = 100 Hz.

v_A / λ_A = v_B / λ_B ;

λ_B = [v_A / v_B] × λ_A

λ_B = [600 / 500] × 5

λ_B = 6 m

3. For a particular tube, among six harmonic frequencies below 1000 Hz, only four harmonic frequencies are given : 300 Hz, 600 Hz, 750 Hz and 900 Hz. What are the two other frequencies missing from this list?.

a) 100 Hz, 150 Hz

b) 150 Hz, 450 Hz

c) 450 Hz, 700 Hz

d) 700 Hz, 800 Hz

Answer : b) 150 Hz, 450 Hz

Solution:

From data let us take open pipe

f₁ : f₂ : f₃ : f₄ : f₅: f₆ = 1 : 2 : 3 : 4 : 5 : 6

f₁ : f₂ : f₃ = f₁ :2 f₁: 3f₁

4. Which of the following options is correct?.

Options for (1), (2) and (3), respectively are

a) (B),(C) and (A)

b) (C), (A) and (B)

c) (A), (B) and (C)

d) (B), (A) and (C)

Answer : a) (B), (C) and (A) 

5. Compare the velocities of the wave forms given below, and choose the correct option.

where, vA, vB, vC and vD are velocities given in (A), (B), (C) and (D), respectively.

a) vA > vB > vD > vC

b) vA< vB < vD < vC

c) vA = vB = vD = vC

d) vA > vB = vD > vC

Answer : c) v_A = v_B = v_D = v_C

6. A sound wave whose frequency is 5000 Hz travels in air and then hits the water surface. The ratio of its wavelengths in water and air is

a) 4.30

b) 0.23

c) 5.30

d) 1.23

Answer: a) 4.30

Solution:

 f_Air = f_water

v_A / λ_A = v_W / λ_W ;

λ_W / λ_A = v_W / v_A = 1493 / 343

λ_W / λ_A = 4.35 = 4.3

7. A person standing between two parallel hills fires a gun and hears the first echo after t1 sec and the second echo after t2 sec. The distance between the two hills is

Answer: d) [v(t₁ + t₂ )] / 2

Solution:

d₁ = vt₁ / 2 ;

d₂ = vt₂ / 2

d = d₁ + d₂

d = [vt₁ / 2] + [vt₂ / 2] ;

d = v [(t₁ / 2) + (t₂ / 2)]

d = [v(t₁ + t₂ )] / 2

8. An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency 83Hz. Then the length of the air column is

a) 1.5 m

(b) 0.5 m

(c) 1.0 m

(d) 2.0 m

Answer : c) 1.0 m

Solution:

f₁ = v / 4L ;

L = v / 4f₁ = 332 / (4 × 83)

L = 332 / 332 = 1.0 m

9. The displacement y of a wave travelling in the x direction is given by y = (2x10-3) sin(300t-2x+π/4), where x and y are measured in metres and t in second. The speed of the wave is

(a) 150 ms-1

(b) 300 ms-1

(c) 450 ms-1

(d) 600 ms-1

Answer : a) 150 ms^-1

Solution:

Δx / Δt = w / k = v

From Q.S w = 300 rads^-1 ;

K = 2

v = Δx / Δt = 300 / 2 = 150 ms^-1

10. Consider two uniform wires vibrating simultaneously in their fundamental notes. The tensions, densities, lengths and diameter of the two wires are in the ratio 8 : 1, 1 : 2, x : y and 4 : 1 respectively. If the note of the higher pitch has a frequency of 360 Hz and the number of beats produced per second is 10, then the value of x : y is

(a) 36 : 35

(b) 35 : 36

(c) 1 : 1

(d) 1 : 2

Answer : a) 36 : 35

Solution:

f ∝1 / l ;

f₁∝1 / l₁ ;

f₂∝1 / l₂

f₁ / f₂ = l₂ / l₁ = y / x

n = | f₁ − f₂ |

⇒ 10 = 360 − f₂

f₂ =350 ;

f₁ =360

y / x = f₁ / f₂ = 360/350 = 36 /35

x / y = 35 /36 

11. Which of the following represents a wave

(a) (x-vt3)

(b) x(x+vt)

(c) 1/(x+vt)

(d) sin(x+vt)

Answer: d) sin(x+vt)

12. A man sitting on a swing which is moving to an angle of 60° from the vertical is blowing a whistle which has a frequency of 2.0 k Hz. The whistle is 2.0 m from the fixed support point of the swing. A sound detector which detects the whistle sound is kept in front of the swing. The maximum frequency the sound detector detected is

(a) 2.027 kHz

(b) 1.974 kHz

(c) 9.74 kHz

(d) 1.011 kHz

Answer : a) 2.027 kHz

13. Let y = 1/(1+x2) at t=0s be the  amplitude of the wave propagating in the positive x-direction. At t = 2 s, the amplitude of the wave propagating becomes 1 / 1+(x-2)2.  Assume that the shape of the wave does not change during propagation. The velocity of the wave is

(a) 0.5ms-1

(b) 1.0ms-1

(c) 1.5ms-1

(d) 2.0ms-1

Answer: b) 1.0m s^-1

Solution:

v = Δx / Δt

From Q.S. Δx = x₁ − x₂ = x − x + 2

Δx = 2 m ;

Δt = 2 s

v = Δx / Δt = 1.0 ms^-1

14. A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. Which of the following plots shows the correct variation of speed v with height h from the lower end?

Answer : d)

15. An organ pipe A closed at one end is allowed to vibrate in its first harmonic and another pipe B open at both ends is allowed to vibrate in its third harmonic. Both A and B are in resonance with a given tuning fork. The ratio of the length of A and B is

(a)  8/3

(b)  3/8       

(c)  1/6

(d)  1/3

Answer: c) 1 / 6

Solution:

v / 4L_A = 3v / 2L_B ;

L_A / L_B = 3v / 12v = 1 / 6 ;

L_A / L_B = 1 / 6

Answers:

1) b   2) d   3) b   4) a

5) c    6) a    7) d   8) c

9) a    10) a  11) d 12) a

13) b 14) d 15) c