Question

A longitudinal wave travels at a speed of 0.3 ms^-1 and the frequency of the wave is 20 Hz. Find the separation between two consecutive compressions
(A) 0.5 cm
(B) 1 cm
(C) 1.5 cm
(D) 2 cm

Answer 1

Hint: Two points undergoing compression or rarefaction together are said to be in the same phase and any two consecutive points which are in the same phase are at a distance of 1 wavelength. The wavelength can be calculated from frequency and speed using the formula \[v{\text{ }} = {\text{ }}f\lambda \], where v denotes speed of the wave, f denotes frequency of the wave and \[\lambda \] denotes wavelength of the wave.

Complete step by step solution:
The wavelength can be calculated using the formula \[v = f\lambda \], where symbols have meanings as described above.
It is given in the question that
Speed of the wave is 0.3 m/s, hence \[v = 0.3m/s\] ,
Frequency of the wave is 20 Hz, hence \[f = 20{\text{ }}Hz\] ,
Using these values in the above formula, we get
\[v = f\lambda \],
\[0.3 = 20\lambda \],
\[\lambda = \dfrac{{0.3}}{{20}}\],
\[\lambda = 0.015\],
Since we used values in SI units, the above calculated value of wavelength is also in SI unit i.e. metres
Converting it to centimeters we get,
\[\lambda = 1.5cm\]
Since the distance between two compressions as explained above is equal to one wavelength, we can say that the required answer is 1.5 cm.

Therefore, the correct answer to the question is option : C

Note: After understanding to solve the problem, the student can also learn that the inverse of frequency is time period. If we replace frequency with inverse of time period in the above formula, i.e.
$f = \dfrac{1}{T}$,
we get,
\[v = \dfrac{\lambda }{T}\].
Comparing this equation with speed = distance / time, we can say that this equation denotes that when a wave travels it covers a distance of one wavelength in one time period.