Question

You have a string with a mass of 0.0127 kg. You stretch the string with a force of 9.33 N, giving it a length of 1.93 m. Then, you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. What is the wavelength of the standing wave you create in the string? What is the frequency?
a. Wavelength = ____________ m
b. Frequency = ____________ Hz

Answer 1

Answer:

wavelength = 0.968 m

frequency = 39.02 Hz

Explanation:

given data

mass = 0.0127 kg

force = 9.33 N

length = 1.93 m

to find out

wavelength and Frequency

solution

we know here linear density that is

linear density = $\frac{mass}{length}$   .........1

linear density = $\frac{0.0127}{1.93}$

linear density = 6.5803 × $10^{-3}$ kg/m

so

wavelength will be here

wavelength = $\frac{2L}{n}$   ..............2

here n = 4 for forth harmonic

wavelength = $\frac{2*1.93}{4}$

wavelength = 0.968 m

and

frequency will be for 4th normal mode of vibration is

frequency = $\frac{4}{2L} \sqrt{\frac{tension}{linear\ density} }$    ..........3

frequency = $\frac{4}{2*1.93} \sqrt{\frac{9.33}{6.5803*10^{-3}} }$

frequency = 1.036269 × 37.654594

frequency = 39.02 Hz