Reflection of inverted waves to form a standing wave

[Vivek98phyboy]

Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?

 

[Ibix]

Shouldn't it be completely destructive interference all the time across the whole length of string?

Clearly not, because we get standing waves.

Have you tried writing down an expression for the sum of two waves moving in opposite directions?

 

[Dale]

If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?

As @Ibix says, the best and easiest way to see this is simply to write it down. Even better if you have plotting software you can use.

 

[A.T.]

Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?

No, because they are traveling in opposite directions, so the phase shift is different at each point. The interference is completely destructive at the anti-nodes of the standing wave.