Question

A sound source is producing 2000 waves in 4 seconds. The loudness and amplitude of this sound wave are 10 dB, and 5 units respectively. Find loudness and frequency of the sound wave when the amplitude is increased to 10 units.​

• A. Loudness = 40 dB; Frequency = 5 Hz
• B. Loudness = 40 dB; Frequency = 5 Hz
• C. Loudness = 50 dB; Frequency = 5 Hz
• D. Loudness = 40 dB; Frequency = 500 Hz

Answer 1

The correct option is D Loudness = 40 dB; Frequency = 500 Hz

We know that frequency of a wave is the number of waves produced in 1 second
Here, No. of waves produced in 4 seconds = 2000
So, No. of waves produced in 1 second = $\frac{2000}{4}=500Hz$
So, the frequency of this sound wave is 500 hertz.

Again,
Initial loudness of the sound ($L_1$)= 10 dB

Initial amplitude ($A_1$) = 5 units
Final amplitude ($A_2$) = 10 units
As we know that,
$Loudness\propto {\left(Amplitude\right)}^{2}Thus,\frac{L_1}{L_2}={\left(\frac{A_1}{A_2}\right)}^2\Rightarrow \frac{10}{L_2}={\left(\frac{5}{10}\right)}^2\Rightarrow L_2=40dB$
Therefore, the frequency of sound wave is 500 Hz and final loudness is 40 dB .