a. What are the three longest wavelengths for standing waves

expeditiupc

expeditiupc

Answered question

2021-12-15

a. On a 240 cm long string with fixed ends, what are the three standing wave wavelengths with the longest wavelengths?
b. If the frequency of the second-largest wavelength is 50.0 Hz, what is the frequency of the third-longest wave length?

Answer & Explanation

Heather Fulton

Heather Fulton

Beginner2021-12-16Added 31 answers

Step 1 
a) Thus, m 1, 2, and 3 will be the three longest wavelengths for standing waves. Thus 
λ1=2(2.40m)1=4.80m 
λ2=2(2.40m)2=2.40m 
λ3=2(2.40m)3=1.60m 
Step 2 
b) Because the wave speed on the string is unchanget from one m value to the other, 
f2λ2=f3λ3f3=f2λ2λ3=(50.0Hz)(2.40m)1.60=75.0Hz

xandir307dc

xandir307dc

Beginner2021-12-17Added 35 answers

Step 1
a) Knowing the formula for the wavelength of a standing wave with fixed nodes at the ends,
λm=2Lm
we can easily get
λ1=2×2401=480m
λ2=2×2402=240cm
λ3=2×2403=160cm
b) We know that the frequency of an m-mode number standing wave is
fm=mf1
Therefore, we have
f3f2=32f3=3f22=75Hz

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