Question

Two sound waves with wavelength $5.0m$ and $5.5m$ respectively, each propagate in a gas with velocity $330m/s$ . We expect the following number of beats per second
(A) $12$
(B) $0$
(C) $1$
(D) $6$

Answer 1

Hint : To solve this question we have to know about wavelengths and frequencies. We know that, in physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda.

Complete Step By Step Answer:
According to the question, we can write the wavelengths are,
${\lambda _1} = 5m$
${\lambda _2} = 5.5m$
So, according to the formula, we can write,
$= \dfrac{v}{{{\lambda _1}}} - \dfrac{v}{{{\lambda _2}}} = 330(\dfrac{1}{5} - \dfrac{1}{{5.5}}) = 66 - 60 = 6$
So the correct option will be D.

Note :
We also have to know that, Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. We also can say, Frequency, the number of waves that pass a fixed point in unit time; also, the number of cycles of periodic motion in unit time. we have to keep these in our mind.