Waves

Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane as shown in the figure. If the mass M is displaced in the horizontal direction, then the frequency of the system is

The equation of a progressive wave is given by y = 5 sin$\left(100 \mathrm{\pi } \mathrm{t} - 0.4 \mathrm{\pi } \mathrm{x}\right)$ where y and x are in m and t is in s

(1) The amplitude of the wave is 5 m.

(2) The wavelength of the wave is 5 m.

(3) The frequency of the wave is 50 Hz.

(4) The velocity of the wave is 250 m s^-1

Which of the following statements are correct?

• (1), (2) and (3)

• (2) and (3)

• (1) and (4)

• All are correct

Assertion:  The fundamental frequency of an open organ pipe increases as the temperature is increased. 

Reason:  This is because as the temperature increases, the velocity of sound increases more rapidly than length of the pipe.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Two waves represented by y = a sin( ωt - kx )  and  y = a cos( ωt- kx ) are superposed. The resultant wave will have an amplitude

• a

• $\sqrt{2} \mathrm{a}$

• 2 a

• zero

Assertion: To hear distinct beats, difference in frequencies of two sources should be less than 10. 

Reason: More the number of beats per sec
more difficult to hear them.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Astronomical wavelength increase due to doppler effect known as

• Red shift

• Voilet shift

• UV

• IR shift

What is your observation when two sources are emitting sound with frequency 499 Hz and 501 Hz?

• Frequency of 500 Hz is heard with change in intensity take place twice.

• Frequency of 500 Hz is heard with change in intensity take place once.

• Frequency of 2 Hz is heard with change in intensity take place once.

• Frequency of 2 Hz is heard with change in intensity take place twice.

A uniform string is vibrating with a fundamental frequency  ' f ' . The new frequency, if radius & length both are doubled would be

•  2f

• 3f

• $\frac{\mathrm{f}}{4}$

• $\frac{\mathrm{f}}{3}$

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2 m long. The length of the open pipe is

• 8 m

• 4 m

• 2 m

• 1 m

Let T₁ and T₂ be the time periods of springs A and B when mass M is suspended from one ·end of each spring. If both springs are taken in series and the same mass M is suspended from the series combination, the time period is T then

• T₁ + T₂ +T₃

• $\frac{1}{\mathrm{T}} = \frac{1}{{\mathrm{T}}_1} + \frac{1}{{\mathrm{T}}_2}$

• T² = ${\mathrm{T}}_1^{ 2} + {\mathrm{T}}_2^{ 2}$

• $\frac{1}{{\mathrm{T}}^2} = \frac{1}{{\mathrm{T}}_1^{ 2}} + \frac{1}{{\mathrm{T}}^2}$