# Wave Speed expression

## Trending Questions

**Q.**A transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following statements, choose the incorrect one.

- Points D, E and F have upward (positive) velocity.
- Points A, B and H have downward (negative) velocity.
- Points A and E have minimum velocity.
- Point C and G have zero velocity.

**Q.**

What is the formula for calculating wave velocity?

**Q.**

What are the effects of the velocity of sound on changing pressure and temperature?

**Q.**

What is the effect of rise in temperature on the velocity of sound?

**Q.**For a plane electromagnetic wave, the magnetic field at a point x and time t is

→B(x, t)=[1.2×10−7sin(0.5×103x+1.5×1011t)^k] T

The instantaneous electric field →E corresponding to →B is (speed of light c=3×108 ms−1)

- →E(x, t)=[−36sin(0.5×103x+1.5×1011t)^j] Vm
- →E(x, t)=[−36sin(1×103x+0.5×1011t)^j] Vm
- →E(x, t)=[36sin(0.5×103x+1.5×1011t)^k] Vm
- →E(x, t)=[36sin(1×103x+1.5×1011t)^i] Vm

**Q.**When a wave travels in a medium, the particle displacement is given by the equation y=asin2π(bt−cx) where a, b and c are constants. The maximum particle velocity will be twice the wave velocity if

- c=1πa
- c=πa
- b=ac
- b=1ac

**Q.**

An electromagnetic wave of intensity $1400\mathrm{W}/{\mathrm{m}}^{2}$ falls on a metal surface on an area $1.5{\mathrm{m}}^{2}$ and is completely absorbed by it. Find the force exerted by the beam.

**Q.**

A hollow pipe of length$0.8m$ is closed at one end. At its open end, a $0.5m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50N$ and the speed of sound is $320m{s}^{-1}$, the mass of the string is

$10g$

$20g$

$40g$

$5g$

**Q.**

A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of 19.2×10 kg m−1. Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2.0 ms−2. Take g=10 ms−2.

**Q.**Intensity of sunlight is observed as 0.092 Wm−2 at a point in free space. What will be the peak value of magnetic field at that point ?

(ε0=8.85×10−12 C2N−1m−2)

- 8.31 T
- 5.88 T
- 2.77×10−8 T
- 1.96×10−8 T

**Q.**A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point 0.5 m distance from lower end will be:

- 5 m/s, 2.24 m/s
- 10 m/s, 3.23 m/s
- 7.5 m/s, 1.2 m/s
- 2.25 m/s, 5 m/s

**Q.**A transverse pulse generated at the bottom of the uniform vertical rope of length L travels in upward direction. The time taken by the pulse to reach the top of the rope will be :

- √L2g
- √2Lg
- √Lg
- √4Lg

**Q.**A simple harmonic wave is represented by the relation

y(x, t)=Asin2x(vt−xλ)

If the maximum particle velocity is three times the wave velocity, the wavelength λ of the wave is

- πA3
- 2πA3
- πA
- πA2

**Q.**

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of 60 cm s−1 when the car accelerates on a horizontal road. Find the acceleration of the car. Take g=10 ms−1.

**Q.**A string (fixed at both ends) of length 1 m has the mass per unit length 0.1 g cm−1. What would be the frequency of vibration of this string for third overtone under the tension of 400 N ?

- 400 Hz
- 50 Hz
- 300 Hz
- 200 Hz

**Q.**In the figure the string has a mass 4.5 g. How much time will it take for a mass for a traverse disturbance produced at the floor to reach the pulley? (Take g=10 ms−2)

- 0.4 s
- 0.04 s
- 20 s
- 0.06 s

**Q.**A transverse wave travelling on a taut string is represented by :

y=0.01sin2π(10t−x)→y and x are in meters and t in seconds. Then

- Closest points on the string which differ in phase by 60∘ are (1/6) m apart.

- The speed of the wave is 10 m/s
- The phase of a certain point on the string changes by 120∘ in (1/20) seconds.

- Maximum particles velocity is π/4 m/s.

**Q.**The angle between wave velocity and particle velocity in a travelling wave (Longitudinal or Transverse wave ) may be (in radians)

- 0
- π4
- π2
- π

**Q.**

Consider two points lying at a distance of $10m$ and $15m$ from an oscillating source. If the periodic time of oscillation is $0.05s$ and the velocity of the wave produced is $300m{s}^{-1}$, then what will be the phase difference between the two points?

$\mathrm{\pi}$

$\frac{\mathrm{\pi}}{6}$

$\frac{\mathrm{\pi}}{3}$

$\frac{2\mathrm{\pi}}{3}$

**Q.**If the magnetic field of a plane electromagnetic wave is given by B=100×10−6sin[2π×2×105(t−xc)] then the maximum electric field associated with it is

(The speed of light =3×108 m/s)

- 6×104 N/C
- 4×104 N/C
- 3×104 N/C
- 4.5×104 N/C

**Q.**

How do you increase the amplitude of a wave?

**Q.**A plane electromagnetic wave, propagating in space, has an electric field of amplitude 9×103 V/m. The amplitude of the magnetic field is,

- 2.7×1012 T
- 9.0×10−3 T
- 3.0×10−4 T
- 3.0×10−5 T

**Q.**A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

**Q.**The equation of a progressive wave for a wire is :

y=4sin[π2(8t−x8)]. If x and y are measured in cm and t is in seconds, then velocity of wave is :

- 64 cm/s along −x direction
- 32 cm/s along −x direction
- 32 cm/s along +x direction
- 64 cm/s along +x direction

**Q.**If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become

- n4
- √2n
- n
- n√2

**Q.**

A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t=t0 is given by g(x, t0)=A sin(xa) . Write the wave equation for a general time t.

**Q.**

A string of mass $3kg$ is under the tension of $400N$. The length of the stretched string is $25cm$. If the transverse jerk is stuck at one end of the string, how long does the disturbance take to reach the other end?

$0.043s$

$0.055s$

$0.034s$

$0.065s$

**Q.**The oscillation frequency of a cyclotron is 10 MHz. What should be the operating magnetic field for accelerating proton?

- 0.156 T
- 0.256 T
- 0.356 T
- 0.656 T

**Q.**

A sound wave of frequency 100 Hz is travelling in air. The speed of sound in air is 350ms−1. (a) By how much is the phase changed at a given point in 2.5 ms? (b) What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the direction of propagation?

**Q.**Distance between the trough and crest of a wave is 1.5 m while distance between two crests is 5 m. Which of the following wavelengths is possible?

- 12, 14, 16, ...
- 1, 2, 3, ...
- 1, 13, 15, ...
- 1, 3, 5, ...