JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Waves & Sound

WhatsApp Email

In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is

____

Answer: 500

Solution

The fundamental frequency of a vibrating string is given by

f = \frac{1}{2 ℓ} \frac{T}{μ}

, where

T

is the tension and

μ

is the linear mass density.

Since the length and linear mass density remain constant, the ratio of frequencies is:

\frac{f _{2}}{f _{1}} = \frac{T _{2}}{T _{1}} = \frac{m _{2} g}{m _{1} g}

Substituting values:

(\frac{50}{30})^{2} = \frac{m}{180}

\frac{25}{9} = \frac{m}{180}

m = \frac{25 \times 180}{9} = 500 g

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Waves & Sound →

More JEE Main questions on Waves & Sound

Two loudspeakers ( $L_{1}$ and $L_{2}$ ) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$ , at equidistance to both loud speakers, is m …
JEE Main 2026View solution →
In an open organ pipe $v_{3}$ and $v_{6}$ are $3^{rd}$ and $6^{th}$ harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200$ Hz then length of the pipe is $____$ mm. (Take velocity of sound in air is $330$ m/s.)
JEE Main 2026View solution →
The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} C$ to $α^{\circ} C$ . The value of $α$ is ______.
JEE Main 2026View solution →
The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is ____.
JEE Main 2026View solution →
A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
JEE Main 2026View solution →
The speed of a longitudinal wave in a metallic bar is $400 m / s$ . If the density and Young's modulus of the bar material are increased by $0.5%$ and $1%$ respectively then the speed of the wave is changed approximately to ______ …
JEE Main 2026View solution →