Oscillation Waves

A sonometer wire of length 1.5 m is made of steel

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10³ kg/m³ and 2.2 × 10¹¹ N/m² respectively?

178.2 Hz
188.5 Hz
200.5 Hz
770 Hz

A pipe of length 85 cm is closed from one end

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A child swinging on a swing in sitting position, stands up

A child swinging on a swing in sitting position, stands up, then the time period of the swing will

Remains same
Decreases
Increases
Increase if the child is tall, decrease if the child is short

A wave y = a sin(ωt − kx) on a string meets with another wave

A wave y = a sin(ωt − kx) on a string meets with another wave producing a node at x = 0. Then the equation of the unknown wave is

y = −a sin(ωt + kx)
y = a sin(ωt + kx)
y = a sin(ωt − kx)
y = −a sin(ωt − kx)

If a spring has time period T, and is cut into n equal parts

If a spring has time period T, and is cut into n equal parts, then the time period of each part will be

T
T√n
nT
T/√n

When a rubber-band is stretched by a distance x

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber band by L is

aL²/2 + bL³/3
(aL² + bL³)/3
aL² + bL³
(aL²/2 + bL³/3)/2

A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps

A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is

286 cps
288 cps
292 cps
294 cps

Length of a string tied to two rigid supports is 40 cm

Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it is

A pipe open at both ends has a fundamental frequency f in air

A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

3f/4
2f
f
f/2