你可以使用下面的代码，我从http://web.archive.org/web/20160111030837/http://developer.android.com/training/permissions/requesting.html复制-

<uses-permission android:name="android.permission.MODIFY_AUDIO_SETTINGS" />

示例：
主要活动

public class MainActivity extends AppCompatActivity {
    private static final int MY_PERMISSIONS_REQUEST_RECORD_AUDIO = 101;
    private ActivityMainBinding mBinding;
    private PermissionRequest myRequest;

    @Override
    protected void onCreate(@Nullable Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        mBinding = DataBindingUtil.setContentView(this, R.layout.activity_main);
        setWebView();
    }

    private void setWebView() {
        mBinding.webView.getSettings().setJavaScriptEnabled(true);
        mBinding.webView.getSettings().setJavaScriptCanOpenWindowsAutomatically(true);
        mBinding.webView.setWebViewClient(new WebViewClient());

        mBinding.webView.getSettings().setSaveFormData(true);
        mBinding.webView.getSettings().setSupportZoom(false);
        mBinding.webView.getSettings().setCacheMode(WebSettings.LOAD_NO_CACHE);
        mBinding.webViemBinding.webView.getSettings().setPluginState(WebSettings.PluginState.ON);

        mBinding.webView.setWebChromeClient(new WebChromeClient() {
            @Override
            public void onPermissionRequest(final PermissionRequest request) {
                myRequest = request;

                for (String permission : request.getResources()) {
                    switch (permission) {
                        case "android.webkit.resource.AUDIO_CAPTURE": {
                            askForPermission(request.getOrigin().toString(),

manifest. permission. RECORD_AUDIO，MY_PERMISSIONS_REQUEST_RECORD_AUDIO）;}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}

mBinding.webView.loadUrl("<your url");
    }

    @Override
    public void onBackPressed() {
        if (mBinding.webView.canGoBack()) {
            mBinding.webView.goBack();
        } else {
            super.onBackPressed();
        }
    }

    @Override
    public void onRequestPermissionsResult(int requestCode,
                                           String permissions[], int[] grantResults) {
        switch (requestCode) {
            case MY_PERMISSIONS_REQUEST_RECORD_AUDIO: {
                Log.d("WebView", "PERMISSION FOR AUDIO");
                if (grantResults.length > 0
                        && grantResults[0] == PackageManager.PERMISSION_GRANTED) {

                    // permission was granted, yay! Do the
                    // contacts-related task you need to do.
                    myRequest.grant(myRequest.getResources());
                    mBinding.webView.loadUrl("<your url>");

                } else {

                    // permission denied, boo! Disable the
                    // functionality that depends on this permission.
                }
            }
            // other 'case' lines to check for other
            // permissions this app might request
        }
    }
    public void askForPermission(String origin, String permission, int requestCode) {
        Log.d("WebView", "inside askForPermission for" + origin + "with" + permission);

        if (ContextCompat.checkSelfPermission(getApplicationContext(),
                permission)
                != PackageManager.PERMISSION_GRANTED) {

            // Should we show an explanation?
            if (ActivityCompat.shouldShowRequestPermissionRationale(MainActivity.this,
                    permission)) {

                // Show an expanation to the user *asynchronously* -- don't block
                // this thread waiting for the user's response! After the user
                // sees the explanation, try again to request the permission.

            } else {

                // No explanation needed, we can request the permission.

                ActivityCompat.requestPermissions(MainActivity.this,
                        new String[]{permission},
                        requestCode);
            }
        } else {
            myRequest.grant(myRequest.getResources());
        }
    }

}

Mainfest.xml:

<uses-permission android:name="android.permission.INTERNET" />
<uses-permission android:name="android.permission.MICROPHONE" />
<uses-permission android:name="android.permission.RECORD_AUDIO" />
<uses-permission android:name="android.permission.INTERNET" />
<uses-feature android:name="android.hardware.audio.low_latency" />
<uses-permission android:name="android.permission.MODIFY_AUDIO_SETTINGS" />
<uses-feature android:name="android.hardware.audio.pro" />
<uses-feature android:name="android.hardware.microphone"/>

Build.gradle:

android {
    compileSdkVersion 26
    defaultConfig {
        applicationId "myapp.example.com.myapplication"
        minSdkVersion 21
        targetSdkVersion 21
        versionCode 1
        versionName "1.0"
    }
    buildTypes {
        release {
            minifyEnabled false
            proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
        }
    }

总而言之，您需要以下组件：

1. MODIFY_AUDIO_SETTINGS权限。
   1.一个WebChromeClient并监听onPermissionRequest的回调
   1.在这个回调函数中，检查request对象中的资源，创建这个request对象的全局变量，迭代并在PermissionRequest类中查找特定的权限，例如PermissionRequest.RESOURCE_VIDEO_CAPTURE，它转换为Manifest.permission.CAMERA权限，检查您的应用是否具有此权限，如果没有，使用任何您希望的机制请求，如果是，请执行4。
   1.在权限回调中，或者如果权限被授予，使用request对象来授予权限ex.request.grant(new String[]{PermissionRequest.RESOURCE_VIDEO_CAPTURE})，这样就可以开始了。
   摘录：

webView.webChromeClient = object: WebChromeClient(){
            override fun onPermissionRequest(request: PermissionRequest?) {
                super.onPermissionRequest(request)

                webkitPermissionRequest = request

                request?.resources?.forEach {
                    when(it){
                        PermissionRequest.RESOURCE_AUDIO_CAPTURE-> {
                            askForWebkitPermission(it, Manifest.permission.RECORD_AUDIO, REQUEST_CODE_PERMISSION_AUDIO)
                        }
                        PermissionRequest.RESOURCE_VIDEO_CAPTURE->{
                            askForWebkitPermission(it, Manifest.permission.CAMERA, REQUEST_CODE_PERMISSION_CAMERA)
                        }
                    }
                }
            }
        }

private fun askForWebkitPermission(webkitPermission: String, androidPermission: String, requestCode: Int){
        val context = activity?: return
        if (context.hasPermission(androidPermission)){
            webkitPermissionRequest!!.grant(arrayOf(webkitPermission))
        }else{
            requestPermissions(arrayOf(androidPermission), requestCode)
        }
    }

希望这个有用。
Google的例子：https://github.com/googlesamples/android-PermissionRequest

重新加载webview的问题，经过太多的研究，发现了这段代码，并创建了下面的代码：

mwebView.setWebChromeClient(new WebChromeClient() {
        @Override
        public void onPermissionRequest(final PermissionRequest request) {
            if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.LOLLIPOP) {
                myRequest = request;
                for (String permission : request.getResources()) {
                    if (permission.equals("android.webkit.resource.AUDIO_CAPTURE")) {
                        demandForPermission(request.getOrigin().toString(), Manifest.permission.RECORD_AUDIO, MY_PERMISSIONS_REQUEST_RECORD_AUDIO);
                    } else {
                        myRequest.grant(request.getResources());
                    }
                }
            }
        }

        @Override
        public void onPermissionRequestCanceled(PermissionRequest request) {
            super.onPermissionRequestCanceled(request);
        }

此链接中的更多信息**Android Webview**