Question

What are the three longest wavelengths for standing soundwaves in a 122-cm-long tube under the following conditions.

a)The tube is open at both ends.
Enter your answers in descendingorder separated by commas. (answer in m)
b)The tube is open at one end, closed at theother?
Enter your answers in descendingorder separated by commas. (answer in m)

Answer 1

Answer:

a)

2.44 m, 1.22 m, 0.81 m

b)

4.88 m, 1.63 m, 0.98 m

Explanation:

a)

$L$ = length of the long tube = 122 cm = 1.22 m

Wavelength for an open pipe is given as

$\lambda = \frac{2L}{n}$

for n = 1

$\lambda = \frac{2(1.22)}{1}\\\lambda = 2.44 m$

for n = 2

$\lambda = \frac{2(1.22)}{2}\\\lambda = 1.22 m$

for n = 3

$\lambda = \frac{2(1.22)}{3}\\\lambda = 0.81 m$

b)

$L$ = length of the long tube = 122 cm = 1.22 m

Wavelength for a pipe open at one end is given as

$\lambda = \frac{4L}{(2n - 1)}$

for n = 1

$\lambda = \frac{4(1.22)}{(2(1) - 1)}\\\lambda = 4.88 m$

for n = 2

$\lambda = \frac{4(1.22)}{(2(2) - 1)}\\\lambda = 1.63 m$

for n = 3

$\lambda = \frac{4(1.22)}{(2(3) - 1)}\\\lambda = 0.98 m$