Consider a string of length 180 cm fixed at both ends. a) What are the three lon
ID: 1386988 • Letter: C
Question
Consider a string of length 180 cm fixed at both ends. a) What are the three longest possible wavelengths for standing waves for this string? b) The frequency of the second-longest wavelength is 70 Hz. What is the frequency of the third-longest wavelength? c) What is the speed of the wave when the frequency is 70 Hz? When the wavelength is the third-longest wavelength? A wave is described by the expression y = (1.8 cm) sin [(0.44/cm) x - (72/s) t] a) Write the equation for a second wave that, when combined with this wave, will produce a standing wave. b) Write the expression for the standing wave produced by the two waves.Explanation / Answer
L = 180 cm = 1.8 cm
at the two fixed ends, nodes will be formed
so distance between the ends = n*?/2 = L
? = 2L/n
n = 1 , 2, 3 ,4, .............
1)
n= 1 ?1 = (2*1.8)/1 = 3.6 m
n = 2 ?2 = (2*1.8)/2 = 1.8 m
n = 3 ?3 = (2*1.8)/3 = 1.2 m
b) f2 = v/?2
f3 = v/?3
f3 = f2*(?2/?3) = 70*(1.8/1.2) = 105 Hz
c) v = ?2*f2 = 126 m/s
V = ?3*f3 = 126 m/s
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(2)
a) y = (1.8cm) sin[ (0.44/cm)x + (72/s)t ]
b) y = (3.6cm) cos(0.44/m)x cos((72/s)t)