(1) A string of constant thickness and length I cm is stretched by a force of T Newton. A tuning fork stamped 256 Hz sets the string vibrating at its fundamental frequency.
Find the frequency of the string when:
(i) Its length is doubled and the tension constant;
(ii) the tension is doubled and the length constant.
2) State the effect of increase in the tension on a wire on its frequency.

Explanation:

i) frequency is the square root of the quotient of Tension over linear density/ all divided by two times the length.

linear density and tension are constant, so the numerator remains constant

The length is doubled, so the frequency is halved.

f = 128 Hz

ii) Doubling the tension increases the frequency by √2

f = 256√2 = 362 Hz

2) If other factors remain constant, increasing tension increases frequency.