Choose the correct option. If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is ______.

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If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is 357 m/s. Explanation: • Express the equation for beat frequency for the first pipe. delta_1 = v/(2l_1) Here, delta_1 is the beat frequency of the first pipe, v is the speed of sound, l_1 is the length of the first pipe. • Substitute 50 cm for l_1 to obtain the beat frequency. delta_1 = v/(2 xx 50 cm) • Express the equation for beat frequency for the second pipe. delta_2 = v/(2l_2) Here, delta_2 is the beat frequency of the second pipe, v is the speed of sound, l_2 is the length of the second pipe. • Substitute 51 cm for l_2 to obtain the beat frequency. delta_1 = v/(2 xx 51 cm) • Express the equation for the beat difference delta = delta_1 - delta_2 Here, delta_1 is the beat frequency of the first pipe and delta_2 is the beat frequency of the second pipe. • Substitute v/(2 xx 50 cm) for delta_1, v/(2 xx 51 cm) for delta_2 and 7 for delta to obtain the value of the speed of sound. 7 = `v/(2 xx 50 cm) - v/(2 xx 51 cm) v = (7 xx 2 xx 50 xx 2 xx 51)/(2 xx 51 - 2 xx 50)` v = 357 m/s

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