# SHM

## Trending Questions

**Q.**At t=0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a long wire is described by the function, y=6x2, given that x≠0. Transverse velocity of a particle at 2 m and at 2 s will be

- 3 m/s upwards
- 3 m/s downwards
- 8 m/s upwards
- 8 m/s downwards

**Q.**A point mass oscillates along the x−axis according to the law x=x0cos(ωt−π/4). If the acceleration of the particle is written as a=Acos(ωt+δ), then

- A=x0, δ=−π/4
- A=x0ω2, δ=π/4
- A=x0ω2, δ=3π/4
- A=x0ω2, δ=−π/4

**Q.**A plane progressive wave is represented by the equation Y=0.1 sin (200π t−20π x17) where y is displacement in m, t in second and x is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are

- 100 Hz, 1.7 m, 170 m/s
- 80 Hz, 1.1 m, 90 m/s
- 120 Hz, 1.25 m, 207 m/s
- 150 Hz, 2.4 m, 200 m/s

**Q.**Which of the following is not true for this progressive wave y=4 sin 2π (t0.02−x100) where y and x are in cm & t in sec

- Its amplitude is 4 cm
- Its frequency is 50 cycles/sec
- Its propagation velocity is 50 x 10
^{3}cm/sec - Its wavelength is 100 cm

**Q.**The equation of progressive wave in a wire is given by y=0.15 sin[2π(15t−x10)]

Where the distance is in meters and time in seconds.

Determine i) amplitude, ii) frequency, iii) wavelength and iv) velocity of the wave

- A=0.1 m, f=15 Hz, v=15 m/s, λ=1 m
- A=0.15 m, f=150 Hz, v=150 m/s, λ=1 m
- A=0.15 m, f=15 Hz, v=150 m/s, λ=10 m
- A=0.15 m, f=30 Hz, v=15 m/s, λ=10 m

**Q.**The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m, 333 m/s, and 110 Hz. Write the equation of the wave.

- y=0.05 sin 110(t−x333)
- y=0.05 sin 110π(t−x333)
- y=0.05 sin 220(t−x333)
- y=0.05 sin 220π(t−x333)

**Q.**The string of a musical instrument is 90 cm long and has a fundamental frequency of 124 Hz. The distance x from one end of the string where it should be pressed to produce a fundamental frequency of 186 Hz

- 50 cm
- 45 cm
- 75 cm
- 60 cm

**Q.**y(x, t)=0.8/[(4x+5t)2+5] represents a moving pulse, where x and y are in metres and t is in seconds, then

- pulse is moving in +x direction
- in 2 s it will travel a distance of 2.5 m
- its maximum displacement along y-axis is 0.16 m
- it is a symmetric pulse

**Q.**Beats are produced by two waves y1=asin200πt and y2=asin208πt. The number of beats heard per second is

- 1
- 0
- 4
- 8

**Q.**A transverse wave is represented by:

y=10πsin(2πT+2πλX)For what value of the wavelength the wave velocity is twice the maximum particle velocity?

- 40 cm
- 20 cm
- 10 cm
- 60 cm

**Q.**A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to:

- 10.0 cm
- 33.3 cm
- 16.6 cm
- 20.0 cm

**Q.**

The given figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

1.0 ms−1

1.5 ms−1

2.0 ms−1

2.5 ms−1

**Q.**The transverse wave propagating through a medium is given by y=Acos2π[ft−xλ]. If maximum particle velocity of medium is two times the velocity of wave through medium, then.

- λ=3.14A
- λ=6.28A
- 6.28λ=A
- 3.14λ=A

**Q.**A transverse wave is described by the equation y=y0sin2π(ft−πλ). The maximum particle velocity is equal to four times the wave velocity if :

- λ = πy04
- λ = πy02
- λ = 2πy0
- λ = πy0

**Q.**Two second sources produce progressive waves given by y1=12cos100πt and y2=4cos102πt neat the ear of an observer. When sounded together, the observer will hear.

- 2 beats per two sound source with an intensity ratio of maximum to minimum nearly 4:1
- 1 beat per second with an intensity ratio of maximum to minimum nearly √2:1
- 1 beats per second with an intensity ratio of maximum to minimum nearly 9:1
- 1 beat per second with an intensity ratio of maximum to minimum nearly 4:1

**Q.**A progressive wave of frequency 500 Hz is travelling with a velocity 360 ms−1. How far are two points 60∘ out of phase?

- 0.12 m
- 0.18 m
- 0.06 m
- 0.24 m

**Q.**A point mass oscillates along the x−axis according to the law x=x0cos(ωt−π/4). If the acceleration of the particle is written as a=Acos(ωt+δ), then

- A=x0, δ=−π/4
- A=x0ω2, δ=π/4
- A=x0ω2, δ=−π/4
- A=x0ω2, δ=3π/4

**Q.**Standing waves are setup in a string of length 240 cm clamped horizontally at both ends. The separation between any two consecutive points were displacement amplitude is 3√2 cm is 20 cm. The standing waves were setup by two travelling waves of equal amplitude of 3 cm. The overtone in which the string is vibrating will be :

- 5th
- 2nd
- 3rd
- 4th

**Q.**If the slope is s, wave velocity is vw and particle velocity of vp then

- vp=svw
- vp=−vws
- vp=−svw
- vp=vws

**Q.**A transverse sinusoidal wave moves along a string in the positive x−direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 0.05 m is

- √3π50 ^j m/s
- −√3π50 ^j m/s
- √3π50 ^i m/s
- −√3π50 ^i m/s

**Q.**(b) If the pipe is filled with air at pressure 1.00×105 Pa and density 1.20kg/m3, what will be the amplitude A and wavelength λ of a longitudinal wave with intensity 3.00×10−6W/m2 and frequency 3400 Hz?

**Q.**A point mass oscillates along the x−axis according to the law x=x0cos(ωt−π/4). If the acceleration of the particle is written as a=Acos(ωt+δ), then

- A=x0, δ=−π/4
- A=x0ω2, δ=π/4
- A=x0ω2, δ=−π/4
- A=x0ω2, δ=3π/4

**Q.**In brass, the velocity of longitudinal waves is 100 times the velocity of transverse waves. If Y=1×1011 N/m2, then the stress in the wire is

- 107/N/m2
- 108/N/m2
- 109/N/m2
- 1010/N/m2

**Q.**Two waves y1=8sin(2x−3t) and y2=6sin(2x−3t−π2) are superimposed. Then, which of the following is/are correct.

(y1 and y2 are in cm)

- Phase difference between y1 and y2 is π2.
- Velocity of y1 and y2 is 1.5 cm s−1
- Amplitude of resultant wave is 20 cm.
- Amplitude of resultant wave is 12 cm.

**Q.**The equation of a light wave is written as y=Asin(kx−ωt). Here, y represents:

- displacement of either particles
- density of the medium
- Pressure in the medium
- electric field

**Q.**Oscillation of a 600Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 400m/s. The standing wave has four loops and an amplitude of 2.0mm. What is the length of the string?

**Q.**A plane progressive wave is given by y=25cos(2πt−πx) Then the amplitude and frequency are respectively

- 25, 100
- 25, 1
- 25, 2
- 50π, 2

**Q.**Three consecutive resonant frequencies of string are 90, 150 and 210Hz. If the length of the string is 80cm what is the speed of the transverse wave in the string ?

- 45m/s
- 48m/s
- 80m/s
- 96m/s

**Q.**The average value of the wave-form shown in the figure above is

- 15√2
- 10√2
- 10
- 15

**Q.**Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed vA and on B with speed vB. The ratio vA/vB is

- 2
- 1/2
- 1/4
- 4