Question

A stationary source (see figure) emits sound waves of frequency $f$ towards a stationary wall. If an observer moving with speed u in a direction perpendicular to the wall measures a frequency $f' = \frac{11}{8} f$ at the instant shown, then $u$ is related to the speed of sound $V_S$ as

• A. $\frac{3}{4} Vs$
• B. $\frac{3}{8} Vs$
• C. $\frac{1}{4} Vs$
• D. $\frac{8}{3} Vs$

Answer 1

Answer: (B)

$\frac{3}{8} Vs$

Answer 2

When energy leaves a sound source, it causes patterns of disturbances called sound waves. Sound is the vibration that travels through a material like a gas, liquid, or solid as an audible wave of pressure.

A sound is a type of wave that travels through a medium at various frequencies until it reaches our ears and is audible to us. A sound is a type of vibration that travels through a medium as mechanical waves. Solid, liquid, and gaseous media all allow for the propagation of sound waves. Compared to liquid and gaseous media, the solid medium allows sound waves to move more quickly.

Sound waves can be defined as The patterns of disturbances that are caused by the movement of energy travelling via a medium

• It is a technique for moving energy in the form of longitudinal mechanical waves from one location to another.
• Sound waves cannot travel in a vacuum and need a medium to do so.
• When a disturbance occurs in a medium, sound waves are created, and sound waves move longitudinally, which means that the vibration of the particles is parallel to the direction of the transmission of the energy wave.
• A zone of high and low pressure is created in the medium as a result of the particle motion.
• Compression and rarefaction are terms used to describe the high-pressure and low-pressure zones, respectively.

These areas transfer to a different medium, which is also responsible for the sound's transmission there.

Some important terms and formulae related to sound waves are mentioned below:

• Period: The time required to complete the one cycle by sound waves, is denoted by T.
• Frequency: It is the number of cycles completed by sound waves in one second, denoted by nu(v). Formula: Frequency = 1/T
• Wavelength (λ): It is the distance covered between two compressions and the rarefaction of sound waves. Formula: Wavelength (λ) = v/F
• Amplitude: It is the maximum distance traveled by the particle on either side of the compression and interaction of the sound waves