A 1.6m long string fixed at both ends vibrates at its fundamental frequency... (i)what is this frequency?

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A 1.6m long string fixed at both ends vibrates at its fundamental frequency... (i)what is this frequency?

For the first part, we consult the formula c=fλ. This tells us that wavelength is inversely proportional to frequency.. ie as one increases the other decreases. This means the lowest(fundamental) frequency goes with the longest wavelength. If you consult a diagram of a vibrating string, you'll see that the greatest wavelength is equal to twice the length of the string.(This is because there must be a node at each end, and is best shown with diagrams).

So the wavelength we are looking for is 1.6x2= 3.2m. Since this is a sound wave c=340m/s. All our numbers are in the correct units, so we may proceed, using f=cλ. The answer is f=106.25Hz

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