Calculating the fundamental frequency of a travelling wave

• savva
In summary, the conversation revolves around a question about the equation of a traveling transverse wave and its relevance to a string under tension. The equation is provided, as well as some background information on the string's tension and linear density. The question then asks for the fundamental frequency and length of the string. Some discussion about deriving the result from first principles is mentioned, and it is noted that a traveling wave does not have a "fundamental frequency" but rather a resonance. The coefficients in the wave equation provide the necessary information to calculate the frequency and wavelength of the wave. It is also mentioned that for the wave to resonate on the string, the string length must be a half wavelength.

savva

No idea what to do here, really tough question, can i get some assistance please?

Homework Statement

The equation of a traveling transverse wave is
y=2.0sin 2π(x/30 - t/0.01)

where x and y are in centimetres and t is in seconds.

When attached at both ends, a string under a tension of 480 N and having a linear density of 1.20 x 10-2 kg/m resonates at a frequency of 150 Hz. The next highest frequency at which the string resonates is 200 Hz.

(i) What is the fundamental frequency of vibration for this string under this tension?

(ii) What is the string’s length?

savva said:
The equation of a traveling transverse wave is
y=2.0sin 2π(x/30 - t/0.01)

where x and y are in centimetres and t is in seconds.

What does this have to do with the rest of the question??

Also, for the question, are you supposed to derive the result from first principles, or just put in the values to the equation? Since you haven't written the equation for this situation, I'm guessing you're supposed to derive it from first principles... Have you been taught how to do that in class?

I could be picky and say that a traveling wave doesn't have a "fundamental frequency". A fundamental frequency implies a resonance which can only occur with a wave that is constrained to have multiple reflections (a standing or stationary wave). Of course, this can be considered as a wave traveling many times up and down the length of string / organ pipe / radio antenna but the modes are defined by the boundaries at each end as well as the wavelength.

The coefficients in the wave equation you are given will tell you the wavelength and the frequency. From that, you can calculate the speed and that is all you need to know about the wave. Look at the general equation for a traveling wave (all over the place for you to find) and the numbers 30 and 0.01 will give you the frequency and wavelength if you compare your equation with the one you find.

For the wave to resonate on the string, you need a whole number of half wavelengths. The fundamental will be when the string length is a half wavelength.
Try to take it from there rather than being given the whole answer in one go.

What is the definition of fundamental frequency?

The fundamental frequency is the lowest frequency of a periodic waveform. It is also known as the first harmonic and determines the pitch of a sound.

How is the fundamental frequency calculated?

The fundamental frequency can be calculated by dividing the speed of the wave by its wavelength. This can be represented by the equation f = v/λ, where f is the fundamental frequency, v is the speed of the wave, and λ is the wavelength.

What factors affect the fundamental frequency of a travelling wave?

The fundamental frequency of a travelling wave is affected by the medium through which it is travelling, the length of the wave, and the tension or stiffness of the medium. These factors can alter the speed and wavelength of the wave, thus changing the fundamental frequency.

How is the fundamental frequency related to harmonics?

The fundamental frequency is the first harmonic of a wave. As the frequency of a wave increases, it produces higher harmonics, which are whole number multiples of the fundamental frequency.

Why is calculating the fundamental frequency important?

Calculating the fundamental frequency allows us to determine the pitch of a sound or the frequency of a wave. It is also important in music, as it helps musicians tune their instruments to the correct frequency for a specific note or key.