Engineering Questions with Answers - Multiple Choice Questions

# Longitudinal Waves

1 - Question

The displacement of a particle varies according to the relation
x=4(cosπt+sinπt)
The amplitude of the particle is?
a) -4
b) 4
c) 4√2
d) 8

Explanation: x=4(cosπt+sinπt)
x=4√2 (sin⁡(π/4)cosπt+cos⁡(π/4)sinπt)
x=4√2 sin⁡(πt+π/4)
Clearly, amplitude=4√2.

2 - Question

The displacement y of a particle in a medium can be expressed as
y=10-6 sin⁡(100t+20x+π/4)
Where t is in seconds and x in meter. The speed of the wave is?
a) 2000m/s
b) 5m/s
c) 20m/s
d) 5πm/s

Explanation: y=10-6 sin⁡(100t+20x+π/4)
Comparing with standard equation,
y=asin⁡(ωt+kx+φ0)
v=ω/k=100/20=5m/s.

3 - Question

The displacement y of a wave travelling in the x direction is given by
y=10-4 sin⁡(600t-2x+π/3)
Where x is expressed in meters and t is seconds. The speed of the wave motion (in m/s) is?
a) 300
b) 600
c) 1200
d) 200

Explanation: y=10-4 sin⁡(600t-2x+π/3)
y=asin⁡(ωt-kx+π/3)
v=ω/k=600/2=300m/s.

4 - Question

A wave y=asin(ωt-kx), on a string meets with another wave producing a node at x = 0. Then, the equation of the unknown wave is?
a) y=asin⁡(ωt+kx)
b) y=-asin⁡(ωt+kx)
c) y=asin⁡(ωt-kx)
d) y=-asin⁡(ωt-kx)

Explanation: For producing node, the superposing wave must travel in the opposite direction (x term must have opposite sign) and its displacement must be negative. Hence the correct option is y=-asin⁡(ωt+kx)
Moreover,
y=y1+y2=asin⁡(ωt-kx)-asin⁡(ωt+kx)
y=-2acosωtsinkx
At x=0, y = 0. That is a node is formed.

5 - Question

The speed of sound in oxygen (O2) at a certain temperature is 460m/s. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal).
a) 460m/s
b) 500m/s
c) 650m/s
d) 1420m/s

Explanation: vHe/v(O2) = √(γHe/γ(O2) ×M(O2)/MHe)=√((5/3)/(7/5)×32/4)=√(200/21)
=√9.52=3.086
vHe=3.086v(O2)=3.086×460=1420m/s.

6 - Question

Length of a string tied to two rigid supports is 40cm. Maximum length (wavelength in cm) of a stationary wave produced on it is?
a) 20
b) 80
c) 40
d) 120

Explanation: When the string vibrates in one segment,
L=ʎ/2
ʎ=2L=2×40=80cm.

7 - Question

A metal wire of linear mass density of 9.8/gm is stretched with a tension of 10kg wt between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance, when carrying an alternating current of frequency v. The frequency v of the alternating source is?
a) 50 Hz
b) 100 Hz
c) 200 Hz
d) 25 Hz

Explanation: Here, m=9.8/gm=9.8×10-3 kg/m
T=10kg wt = 9.8×10=98N
L=1m
The fundamental frequency of vibration of the string,
v=1/2L×√(T/m)=1/2×√(9.8/(9.8×10-3))=50Hz.

8 - Question

A sound absorber attenuates the sound level by 20dB. The intensity decreases by a factor of ____________
a) 100
b) 1000
c) 10000
d) 10

Explanation: L1=10log⁡(I1/I0) L2=10log⁡(I2/I0)
I1-I2=10log⁡(I1/I2)
20dB=10log⁡(I1/I2)
I1/I2 = 102 I2=1/100×I1.

9 - Question

The ratio of velocity of sound in hydrogen and oxygen at STP is __________
a) 16:1
b) 8:1
c) 4:1
d) 2:1

Explanation: vH/vO = √(MO/MH)=√(32/2)=4:1.

10 - Question

It takes 2 seconds for a second wave to travel between two fixed points when the day temperature is 10°C. If the temperature rises to 30°C, the sound wave travels between the same fixed parts in __________
a) 1.9 sec
b) 2 sec
c) 2.1 sec
d) 2.2 sec