To determine which wave has the lowest frequency, we can use the formula for frequency (f):
\[ f = \frac{v}{\lambda} \]
where \( v \) is the speed of the wave, and \( \lambda \) is the wavelength.
Since all the waves listed have the same speed \( v = 600 , \text{m/s} \), we can simply calculate the frequency for each wave using their respective wavelengths:
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For wave L (\( \lambda = 120 , \text{m} \)): \[ f_L = \frac{600}{120} = 5 , \text{Hz} \]
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For wave M (\( \lambda = 150 , \text{m} \)): \[ f_M = \frac{600}{150} = 4 , \text{Hz} \]
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For wave N (\( \lambda = 100 , \text{m} \)): \[ f_N = \frac{600}{100} = 6 , \text{Hz} \]
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For wave O (\( \lambda = 50 , \text{m} \)): \[ f_O = \frac{600}{50} = 12 , \text{Hz} \]
Now we can compare the frequencies:
- Wave L: 5 Hz
- Wave M: 4 Hz
- Wave N: 6 Hz
- Wave O: 12 Hz
The wave with the lowest frequency is wave M with a frequency of 4 Hz.
So, the answer is: wave M