Question

What are (a) the lowest frequency, (b) the second lowest frequency, and (c) the third lowest frequency for standing waves on a wire that is 10.0 m long, has a mass of 100 g, and is stretched under a tension of 250 N

Answer 1

Answer:

$a. \ f_1=7.9057Hz\\\\b. \ f_2=15.8114Hz\\\\c. \ f_3=23.7171Hz$

Explanation:

a. The wire's length is 10m long and has a mass 100g and a tension of 250N.

Frequency is given by the equation:

$f=\frac{nv}{2L}\\\\=\frac{n}{2L}\sqrt{\frac{t}{\mu}$ #where t=250N*10=2500N, $\mu=0.1kg$

#substitute for actual values for the lowest frequency.

$F=\frac{n}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=\frac{1}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=7.9057Hz$  #n=1, lowest frequency

Hence, the lowest frequency for standing waves is 7.9057Hz

b.The wire's length is 10m long and has a mass 100g and a tension of 250N.

Frequency is given by the equation:

$f=\frac{nv}{2L}\\\\=\frac{n}{2L}\sqrt{\frac{t}{\mu}$           #where t=250N*10=2500N,$\mu=0.1kg$

#The second lowest frequency happens at $n=2$:

$F=\frac{n}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=\frac{2}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=15.8114Hz$

Hence, the second lowest frequency is 15.8114Hz

c.Given that the wire's length is 10m long and has a mass 100g and a tension of 250N.

Frequency is given by the equation:

$f=\frac{nv}{2L}\\\\=\frac{n}{2L}\sqrt{\frac{t}{\mu}$                    #where t=250N*10=2500N,$\mu=0.1kg$

The third lowest frequency happens at $n=3$

$F=\frac{n}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=\frac{3}{2\times 10m}\times \sqrt{2500N/0.1kg}\\=23.7171Hz$

Hence, the third lowest frequency is 23.7171Hz