Solutions to problems on standing waves

a.) To understand what happens to the frequency of the fundamental standing wave on a string when we change the tension of the string, we need to know

The equation for the wavespeed (V_string) tells us that if we decrease the tension in the string we decrease the wavespeed along the string. The equation for the frequency of the first harmonic tells us that a smaller wavespeed results in a lower fundamental frequency. Hence, reducing the tension decreases the frequency.
b.) By reducing the length of the string by a factor of 2, the equation for the frequency of the first harmonic tells us that frequency of the fundamental will be increased by a factor of 2.
c.) The shapes of the standing waves are as given

c.) The frequency of the second harmonic is twice the frequency of the fundamental. From the information given:

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Last updated: 14 Oct 1999
Comments: bland@indiana.edu