Question

A sound wave has a frequency of $4700Hz$ and travels along a steel rod. If the distance between compressions, or regions of high pressure, is $1.1{\text{m}}$ , what is the speed of the wave?
$A)\;5170{\text{ }}m/s$
$B)\;6270{\text{ }}m/s$
$C)\;5100{\text{ }}m/s$
$D)\;2170{\text{ }}m/s$

Answer 1

Frequency and wavelength are given in the question. we have to find the velocity of the sound wave using the relation between the velocity of sound, its wavelength, and frequency.

Complete step by step answer:
Frequency of sound wave: $4700Hz$
Regions of high pressure (Wavelength): $1.1{\text{m}}$
The relation between velocity of sound,its wavelength and frequency can be given by,
$v = f \times \lambda$
where, $v = {\text{velocity of the wave}}$
$f = {\text{frequency of the wave}}$
$\lambda = {\text{wavelength of the wave}}$
As per the formula, the velocity of sound wave $v = f \times \lambda = 4700 \times 1.1 = 5170m/s$.

Hence the right answer is in option (A).

Additional information:
The relation between wavelength and wave velocity can be derived as shown below,
Wavelength is defined as the distance traveled by the wave during the time a particle of the medium completes one vibration.
Hence, if the wavelength and T the time period then the wave travels a distance and time T.
velocity=Distance/Time
$V = \dfrac{\lambda }{T}$
As we know that $\dfrac{1}{T} = frequency \left( \upsilon \right)$
$V = \upsilon \lambda = frequency \times wavelength$

Note: The frequency of the wave is set by whatever is driving the oscillation in the medium. The velocity of the wave is a property of the medium. The wavelength of the wave is then determined by the frequency and velocity:
$\lambda = \dfrac{\upsilon }{f}$
The wavelength is inversely proportional to the frequency and directly proportional to the velocity of the wave.