Question

The equation of a simple harmonic progressive wave is y = 0.30 sin (314 t– 1.57 x), where tx and y are in second, meter and cm respectively. Calculate the frequency and the wavelength of the wave

Solution

Correct option is

Frequency = 50 second–1 , wavelength = 4m

 

In the equation y = 0.30 sin (314 t – 1.57 x), t is in second, y in cm and x in meter. If y is also expressed in meter, then

                 

                    

                    

Comparing it with the standard equation , we get 

Time-period    T = (1/50) second.

∴ frequency,  n = 1/T = 50 second–1.  

And wavelength, λ = 4 meter.    

SIMILAR QUESTIONS

Q1

A simple harmonic wave-train is travelling in a gas in the positive direction of the X-axis. Its amplitude is 0.04 m, speed is 330 m/s and frequency is 110 Hz. Write down the equation of the wave.

Q2

The equation of the progressive wave is y = 0.5  where yand x are in cm and is in second. What is wave velocity?

Q3

 

The equation of a simple harmonic progressive wave is 

                                   

Where y and x are in cm and t in second. Calculate the amplitude, frequency and speed of the wave and the phase difference between two particles at a distance of 2.0 cm apart at any instant. 

Q4

The equation of motion of a wave is  where the distances are in metre and the time is in second. Determine the amplitude and the frequency of wave, and the maximum velocity of the particle. What are the velocity and the direction of the wave?

Q5

A wave has a speed of 330 metre/second and frequency 500 hertz. The phase difference between two adjacent points is π/3 radian. What will be the path difference between them? 

Q6

The equation of a simple harmonic wave is y1 = 0.40 sin (314 t – 1.57 x) meter, and that of another similar wave is y2 = 0.20 sin (314t – 1.57x + 1.57) meter. Find the phase difference between these two waves and the ratio of their intensities. 

Q7

In the figure given below is shown displacement-distance (y – x) graph of a transverse wave travelling along a string at the instant t = 0.25 s. At the instant t = 0, the end A of the string was in the mean position. Find out: (i) Frequency, wave-length and velocity of the wave, (ii) Equation of the wave, (iii) Displacement of B at the instant t = 1 second.

                                               

Q8

A transverse harmonic wave is travelling on a string with a speed of 25 m/s. A particle on the string has maximum velocity and maximum acceleration 4 m/s and 100 m/s2 respectively. What is the waveform?

Q9

A wave whose amplitude is 0.07m and frequency is 400 hertz travels in a medium with a velocity of 300 m/s. Determine the displacement equation of oscillation at a distance x metre from the source due to this wave.

Q10

What do you know about the speed of red and blue light (i) In vacuum, (ii) In glass? The refraction index of glass for blue light is 1.665 and for red light is 1.645. (The speed of light in vacuum is ).