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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
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B
Loudness = 40 dB; Frequency = 5 Hz
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C
Loudness = 50 dB; Frequency = 5 Hz
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D
Loudness = 40 dB; Frequency = 500 Hz
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Solution

## The correct option is D Loudness = 40 dB; Frequency = 500 HzWe 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 = 20004 = 500 Hz So, the frequency of this sound wave is 500 hertz. Again, Initial loudness of the sound (L1)= 10 dB Initial amplitude (A1) = 5 units Final amplitude (A2) = 10 units As we know that, Loudness ∝ (Amplitude)2 Thus, L1L2 =(A1A2)2 ⇒10L2=(510)2⇒L2 = 40 dB Therefore, the frequency of sound wave is 500 Hz and final loudness is 40 dB .

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