# Help with questions on Sound Waves and Harmoics

1.) A transverse wave is travelling with a speed of 300m/s on a horizontal string. If the tension in the string is increased by a factor of four, what is the speed of the wave?

2.) A wire has a cross-sectional area of 4.2 X 10-8 m2 and is made from a material whose density is 7900 kg/m3. Determine the wire's linear density (m/L).

3.) A uniform cord has a mass of 0.300 kg and a total length of 6.00 m. Tension is maintained in the cord by suspending a 2.00 kg mass from one end. Find the speed of a pulse on this cord. Assume the tension is not affected by the mass of the cord.

4.) A middle C string of the C-major scale on a piano has a fundamental frequency of 262 Hz. And the A note has a fundamental frequency of 440 Hz.

a.) Calculate the frequencies of the next two harmonics of the C string.

b.) If the strings for the A and C notes are assumed to have the same mass per unit length and the same length, determine the ratio of tensions in the two strings.

c.) In a real piano, the assumption we made in (b) is only half true. The string densities are equal, but the A string is 64% as long as the C string. What is the ratio of their tensions?