Waves Questions

The displacement $y$ of a particle in a medium can be expressed as $y=10^{-6}\sin (100t+20x+\pi /4)\text{m}$, where $t$ is in seconds and $x$ in meter. The speed of the wave is:

A whistle producing sound waves of frequencies $9500\text{Hz}$ and above is approaching a stationary person with speed $v\text{m/s}$. The velocity of sound in air is $300\text{m/s}$. If the person can hear frequencies up to a maximum of $10000\text{Hz}$, the maximum value of $v$ up to which he can hear the whistle is:

A string is stretched between fixed points separated by $75\text{cm}$. It is observed to have resonant frequencies of $420\text{Hz}$ and $315\text{Hz}$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is:

A sound absorber attenuates the sound level by $20\text{dB}$. The intensity decreases by a factor of:

The function ${\sin }^2(\omega t)$ represents:

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously, $4$ beats per second are heard. Now, some tape is attached on the prong of the fork $2$. When the tuning forks are sounded again, $6$ beats per second are heard. If the frequency of fork $1$ is $200\text{ Hz}$, then what was the original frequency of fork $2$?

An observer moves towards a stationary source of sound, with a velocity one fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

A metal wire of linear mass density $9.8\text{g/m}$ is stretched with a tension of $10\text{kg-wt}$ between two rigid supports $1\text{metre}$ apart. The wire passes at its middle point between the poles of a magnet and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is:

A tuning fork of known frequency $256\text{Hz}$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:

The displacement $y$ of wave travelling in the $x$ -direction is given by $y=10^{-4}\sin (600t-2x+\pi /3)$ metres, where $x$ is in metres and $t$ in seconds. The speed of the wave-motion in $\text{m/s}$ is:

A motor cycle starts from rest and accelerates along a straight path at $2{\text{m/s}}^2$. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motor cycle was at rest? (speed of sound $=330{\text{m s}}^{-1}$).

Three sound waves of equal amplitudes have frequencies $(\nu -1)$, $\nu$, $(\nu +1)$. They superpose to give beats. The number of beats produced per second will be:

The equation of a wave on a string of linear mass density $0.04{\text{kg m}}^{-1}$ is given by $y=0.02(m)\sin [2\pi (\frac{t}{0.04(s)}-\frac{x}{0.50(m)})]$. The tension in the string is:

The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t)=e^{-(a{x}^2+b{t}^2+2\sqrt{ab}xt)}$. This represents a: