A sound wave of frequency 500 Hz travels between two points $X$ and $Y$ separated by a distance of 600 m in a time of 2 s . The number of waves between the points $X$ and $Y$ are

The equation of a transverse wave propagating along a stretched string of length 80 cm is $y=1.5 \sin \left\{\left(5 \times 10^{-3} x\right)+20 t\right\}$, here ' $x$ ' and ' $y$ ' are in cm and the time ' $t$ ' is in second. If the mass of the string is 3 g , then the tension in the string is 80 cm

If a travelling wave is given by $y(x, t)=0.5 \sin (70.1 x-10 \pi t)$, where $x$ and $y$ are in metre the time $t$ is in second, then the frequency of the wave is

The path difference between two waves given by the equations

$y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and $y_2=a_2 \sin \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is

If two progressive sound waves represented by $y_1=3 \sin 250 \pi t$ and $y_2=2 \sin 260 \pi t$ (where displacement is in metre and time is in second) superimpose, then the time interval between two successive maximum intensities is

In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively

When a stretched wire of fundamental frequency $f$ is divided into three segments, the fundamental frequencies of these three segments are $f_1, f_2$ and $f_3$ respectively. Then the relation among $f_1, f_2, f_3$ and $f$ is (Assume tension is constant)

A steel wire of length 81 cm has a mass of $5 \times 10^{-3} \mathrm{~kg}$.

If the wire is under a tension of 50 N , then the speed of transverse waves on the wire is

The speed of a stationary wave represented by the equation

$ y=0.7 \sin \left(\frac{7 \pi}{4} x\right) \cos (350 \pi t) \text { is } $

(In the given equation $x$ and $y$ are in metre and $t$ is in second)

Two sound waves of wavelengths 99 cm and 100 cm produce 10 beats in a time of $t$ seconds. If the speed of sound in air is $330 \mathrm{~ms}^{-1}$, then the value of $t$ in seconds is

The fundamental frequency of an open pipe is 100 hz If the bottom end of the pipe is closed and $1 / 3$ rd of the pipe is filled with water, then the fundamental frequency of the pipe is

The vibrations of four air columns are shown below. The ratio of frequencies is

Two cars are moving towards each other at the speed of $50 \mathrm{~ms}^{-1}$. If one of the cars blows a horn at a frequency of 250 Hz , the wave length of the sound perceived by the driver of the other car is

(Speed of sound in air $=350 \mathrm{~ms}^{-1}$)

Speed of sound in air near room temperature is approximately

A body is suspended from a string of length 1 m and mass 2 g. The mass of the body to produce a fundamental mode of 100 Hz frequency in the string is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)

Two waves are represented by $x_1=A \sin \left(\omega t+\frac{\pi}{6}\right) \text { and } x_2=A \cos \omega t \text {. }$ Then, the phase difference between them is

A string fixed at both ends vibrate in 5 loops as shown in the figure. The total number of nodes and anti-nodes respectively are

Match the following.

The sources of sound A and B produce a wave of 350 Hz in same phase. A particle P is vibrating under an influence of these two waves. If the amplitudes at P produced by the two waves is 0.3 mm and 0.4 mm, the resultant amplitude of the point P will be, when AP $-$ BP = 25 cm and the velocity of sound is 350 ms$^{-1}$