JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Waves & Sound

WhatsApp Email

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.

Answer: 152

Solution

Let the frequency of the first fork be

f

.

Since each fork gives 4 beats with the preceding one:

$f_{1} = f$
$f_{2} = f + 4$
$f_{3} = f + 8$
...
$f_{20} = f + 19 \times 4 = f + 76$

Given that

f_{20} = 2 f

f + 76 = 2 f

f = 76 Hz

Therefore, the frequency of the last fork is:

f_{20} = 2 f = 2 \times 76 = 152 Hz

JEE Main · 2022 · 26 Jun 2022 · 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 →