A string is stretched between fixed points separated by \(75.0~\text{cm}.\) It is observed to have resonant frequencies of \(420~\text{Hz}\) and \(315~\text{Hz}\). There are no other resonant frequencies between these two. The lowest resonant frequency for these strings is:

1.	\(155~\text{Hz}\)	2.	\(205~\text{Hz}\)
3.	\(10.5~\text{Hz}\)	4.	\(105~\text{Hz}\)

If n₁, n₂ and n₃ are, are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

(1) 1/n=1/n₁+1/n₂+1/n₃

(2) 1/√n=1/√n₁+1/√n₂+1/√n₃

(3) √n=√n₁+√n₂+√n₃

(4) n=n₁+n₂+n₃

A speed motorcyclist sees a traffic jam ahead of him. He slows down to 36km/h. He finds that traffic has eased and a car moving in front of him at 18km/h is honking at a frequency of 1392Hz. If the speed of sound is 343m/s, the frequency of the honk as heard by him will be 
1. 1332Hz
2. 1372Hz
3. 1412Hz
4. 1454Hz 

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by

(1) y=sin(x-2t)

(2) y=sin(2πx-2πt)

(3) y=sin(10πx-20πt)

(4) y=sin(2πx+2πt)

If we study the vibration of a pipe open at both ends. then the following statements is not true

(1) Open end will be anti-node

(2) Odd harmonics of the fundamental frequency will be generated

(3) All harmonics of the fundamental frequency will be generated

(4) Pressure change will be maximum at both ends

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is

(1) 254 Hz

(2) 246 Hz

(3) 240 Hz

(4) 260 Hz

When a string is divided into three segments of lengths $l_1, l_2 and l_3,$ the fundamental frequencies of these three segments are $v_1, v_2 and v_3$ respectively. The original fundamental frequency (v) of the string is 

(1) $\sqrt{v}=\sqrt{v_1}+\sqrt{v_2}+\sqrt{v_3}$

(2) $v=v_1+v_2+v_3$

(3) $\frac{1}{v}=\frac{1}{v_1}+\frac{{\displaystyle 1}}{{\displaystyle v_2}}+\frac{{\displaystyle 1}}{{\displaystyle v_3}}$

(4) $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_1}}+\frac{{\displaystyle 1}}{{\displaystyle \sqrt{v_2}}}+\frac{{\displaystyle 1}}{{\displaystyle \sqrt{v_3}}}$

Two sources of sound placed close to each other, are emitting progressive waves given by

${\mathrm{y}}_1$=4 sin 600$\mathrm{\pi t}$ and ${\mathrm{y}}_2$=5 sin 608 $\mathrm{\pi t}$

An observer located near these two sources of sound will hear

(a)4 beats per second with intensity ratio 25:16 between waxing and waning

(b) 8 beats per second with intensity ratio 25:16 between waxing and waning

(c) 8 beats per second with intensity ratio 81:1 between waxing and waning

(d) 4 beats per second with intensity ratio 81:1 waxing and waning

The equation of a simple harmonic wave is 

given by 

          $\mathrm{y}=3 \sin \frac{\mathrm{\pi }}{2}(50\mathrm{t}-\mathrm{x})$

where x and y are in meters and t is in 

seconds. The ratio of maximum particle 

velocity to the wave velocity is

(1) $2\mathrm{\pi }$

(2) $\frac{3}{2}\mathrm{\pi }$

(3) $3\mathrm{\pi }$

(4) $\frac{2}{3}\mathrm{\pi }$