If a wave has a period of 30 seconds and the frequency is cut to a quarter, then the new period can be calculated using the formula:
New Period = 1 / New Frequency
The original frequency can be calculated using the formula:
Frequency = 1 / Period
So, for the original wave:
Frequency = 1 / 30 seconds = 0.0333 Hz
When the frequency is cut to a quarter, the new frequency is:
New Frequency = 0.0333 Hz / 4 = 0.00833 Hz
Using the formula for the new period:
New Period = 1 / 0.00833 Hz = 120 seconds
Therefore, the new period is 120 seconds.