The speed of water waves is 30cm/s in deep water & 15cm/s in shallow water. If the wavelength in deep water is 1.0cm, what is the wavelength in shallow water?
(v2/v1)=(wavelength2/wavelength1)
Therefore (15/30)=(wavelength2/1)
- 15=30wavlength2
-Wavelength2=0.5cm/s
A) Is that correct?
B) I'm confident I chose the right values for 1 & 2 because I know that the wavelength gets shorter as the water gets shallower but otherwise, when it's not specified, how do I know what is 2 & what is 1?
Thanks a ton :)
the frequency (and period) do not change)
distance = speed * time
or
wavelength = speed * period
1 = 30 T so T = 1/30
L = 15 T = 15(1/30) = 1/2
so I agree
Ok excellent, thank you :)
A) Yes, your calculation is correct. When comparing the speed of water waves in two different conditions (deep water and shallow water), the relationship between the wavelengths can be determined using the formula you mentioned: v2/v1 = wavelength2/wavelength1.
In this case, you correctly substituted the given values into the formula: (15 cm/s) / (30 cm/s) = wavelength2 / (1.0 cm). Solving for wavelength2 gives you 0.5 cm/s. So, the wavelength in shallow water would be 0.5 cm.
B) When it's not specified which condition is labeled as "2" and which one as "1," you can choose either one arbitrarily. The important thing is to be consistent throughout your calculations. In this case, you chose the speeds (v1 = 30 cm/s, v2 = 15 cm/s) and the wavelength in deep water (wavelength1 = 1.0 cm). Since you correctly applied the formula for the wavelength comparison, it doesn't matter which condition you labeled as "1" or "2" as long as you consistently use those labels in your calculations.
You're welcome! If you have any more questions, feel free to ask.