QUESTION SIX [14 MARKSI (a)Define the terms:- beats and intepsity of sound. (b) A closed pipe has a length of 30cm and end correction of 1cm calculate the fundamental frequency, the next two frequencies after the fundamental frequency and the wavelength of second overtone. (c) At a cocktail party 38 people were speaking equally loudly, if only one person was speaking, the sound level would be 72dB. Find the sound level when all the 38 people were talking.

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QUESTION SIX [14 MARKSI (a)Define the terms:- beats and intepsity of sound. (b) A closed pipe has a length of 30cm and end correction of 1cm calculate the fundamental frequency, the next two frequencies after the fundamental frequency and the wavelength of second overtone. (c) At a cocktail party 38 people were speaking equally loudly, if only one person was speaking, the sound level would be 72dB. Find the sound level when all the 38 people were talking.

Answer 1

(a) Beats: Beats are the periodic variations in the intensity of a sound wave that occur when two waves of slightly different frequencies interfere with each other. The frequency of the beats is equal to the difference between the two frequencies.Intensity of sound: Intensity of sound refers to the power per unit area carried by a sound wave. It is measured in watts per square meter (W/m²) and is a measure of the loudness or volume of the sound.(b) Fundamental frequency: The fundamental frequency of a closed pipe is the lowest frequency at which the pipe resonates. It is determined by the length of the pipe and the speed of sound in the medium. For a closed pipe, the fundamental frequency is given by the formula:f = v / (4L)where f is the fundamental frequency, v is the speed of sound, and L is the length of the pipe.The next two frequencies after the fundamental frequency are the second and third harmonics, which are multiples of the fundamental frequency.Wavelength of the second overtone: The wavelength of the second overtone is twice the length of the pipe, since it is the third harmonic.(c) Sound level: The sound level in decibels (dB) is a logarithmic measure of the intensity of a sound. It is calculated using the formula:L = 10 log10(I/I0)where L is the sound level in dB, I is the intensity of the sound, and I0 is the reference intensity, which is typically the threshold of hearing (10^-12 W/m²).To find the sound level when 38 people are talking, we can use the formula for sound level and the given information that one person speaking produces a sound level of 72 dB.L = 10 log10(38I/I0)Since the sound level is proportional to the logarithm of the number of people, we can use the properties of logarithms to simplify the equation:L = 10 log10(38) + 10 log10(I/I0)Since the sound level for one person is 72 dB, we can substitute this value into the equation:L = 10 log10(38) + 72Using a calculator, we can find that L ≈ 83.5 dB.

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