of the wave Once the speed of propagation is known, the frequency of the sound produced by the string can be calculated. The speed of propagation of a wave is equal to the wavelength divided by the period , or multiplied by the frequency : If the length of the string is , the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so is half of the wavelength of the fundamental harmonic. Hence one obtains Mersenne's laws: where is the tension (in Newtons), is the linear density (that is, the mass per unit length), and is the length of the vibrating part of the string. Therefore: the shorter the string, the higher the frequency of the fundamental the higher the tension, the higher the frequency of the fundamental the lighter the string, the higher the frequency of the fundamental Moreover, if we take the nth harmonic as having a wavelength given by , then we easily get an expression for the frequency of the nth harmonic: And for a string under a tension T with linear density , then Observing string vibrations One can see the waveforms on a vibrating string if the frequency is low enough and the vibrating string is held in front of a CRT screen such as one of a television or a computer (not of an analog oscilloscope). This effect is called the stroboscopic effect, and the rate at which the string seems to vibrate is the difference between the frequency of the string and the refresh rate of the screen. The same can happen with a fluorescent lamp, at a rate that is the difference between the frequency of the string and the frequency of the alternating current. (If the refresh rate of the screen equals the frequency of the string or an integer multiple thereof, the string will appear still but deformed.) In daylight and other non-oscillating light sources, this effect does not occur and the string appears still but thicker, and lighter or blurred, due to persistence of vision. A similar but more controllable effect can be obtained using a stroboscope. This device allows matching the frequency of the xenon flash lamp to the frequency of vibration of the string. In a dark room, this clearly shows the waveform. Otherwise, one can use bending or, perhaps more easily, by adjusting the machine